Metrics for GTR1 distribution

analyze65.0ms (0.7%)

Memory

-17.2MiB live, 66.0MiB 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)

sample2.8s (29.4%)

Memory

-88.8MiB live, 1 758.9MiB allocated

Samples

2.5s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 2.2s

ival-div: 511.0ms (23% of total)

const: 411.0ms (18.5% of total)

ival-<=: 409.0ms (18.4% of total)

ival-mult: 376.0ms (16.9% of total)

ival-sub: 254.0ms (11.4% of total)

ival-log: 119.0ms (5.4% of total)

ival-add: 76.0ms (3.4% of total)

ival-pi: 27.0ms (1.2% of total)

ival-and: 23.0ms (1% of total)

exact: 11.0ms (0.5% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

preprocess364.0ms (3.8%)

Memory

-9.2MiB live, 541.7MiB 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)

explain172.0ms (1.8%)

Memory

27.8MiB live, 312.2MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

52.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 19.0ms (52.4% of total)

ival-log: 6.0ms (16.6% of total)

ival-div: 4.0ms (11% of total)

ival-pi: 2.0ms (5.5% of total)

ival-add: 2.0ms (5.5% of total)

ival-sub: 2.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.5%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify323.0ms (3.4%)

Memory

-32.2MiB live, 468.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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

localize40.0ms (0.4%)

Memory

-10.0MiB live, 66.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.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))))
✓	accuracy	98.7%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

24.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

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

ival-mult: 7.0ms (42.2% of total)

ival-log: 4.0ms (24.1% of total)

ival-div: 2.0ms (12.1% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.5%)

Memory

-4.1MiB live, 74.0MiB allocated

Counts

7 → 132

Calls

Call 1

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

Outputs
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<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))))))))>
#<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))))))))>
#<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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<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))))))))>
#<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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<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))))))))>
#<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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -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)))))>
#<alt (- (+ (* (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)))))>
#<alt (- (+ (* (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)))))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 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))>
#<alt (/ (- (+ (/ 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))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>

Calls

33 calls:

Time	Variable		Point	Expression
28.0ms	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))))

simplify348.0ms (3.7%)

Memory

12.1MiB live, 526.1MiB 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)))
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(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 (PI.f32) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)))))))) (*.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 #s(literal 1 binary32) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 (PI.f32) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))))))) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal 1 binary32) (.f32 (.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)))) (pow.f32 cosTheta #s(literal 6 binary32)))))))) (*.f32 cosTheta cosTheta))
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(pow alpha 2)
(*.f32 alpha alpha)
(* 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 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))

rewrite365.0ms (3.8%)

Memory

4.2MiB live, 635.6MiB allocated

Algorithm

1×	batch-egg-rewrite

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))))
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(/.f32 (+.f32 (pow.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 3 binary32)) (pow.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 3 binary32))) (fma.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha)) (-.f32 (.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta #s(literal -1 binary32))) (.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta #s(literal -1 binary32))))))
(/.f32 (+.f32 (pow.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 3 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32))) (fma.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta) (-.f32 (.f32 (neg.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))))
(/.f32 (-.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha))) (.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta #s(literal -1 binary32)))) (-.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta)) (.f32 (neg.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))
(.f32 #s(literal 1 binary32) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
(.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(*.f32 (fma.f32 alpha cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32)))
(.f32 (.f32 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 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 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) 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)) cosTheta) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))))
(.f32 (/.f32 cosTheta (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (fma.f32 (.f32 alpha alpha) (*.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 alpha #s(literal 1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 cosTheta (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (fma.f32 alpha cosTheta cosTheta)) (+.f32 alpha #s(literal -1 binary32)))
(+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))) (.f32 cosTheta (*.f32 cosTheta #s(literal -1 binary32))))
(+.f32 (.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta)) (.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(+.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) cosTheta) (.f32 (*.f32 cosTheta #s(literal -1 binary32)) cosTheta))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (.f32 (neg.f32 cosTheta) cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(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)))

eval87.0ms (0.9%)

Memory: 5.2MiB live, 239.0MiB allocated
Compiler: Compiled 33 548 to 2 790 computations (91.7% saved)

prune136.0ms (1.4%)

Memory

33.0MiB live, 391.2MiB allocated

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	861	22	883
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	862	22	884

Accuracy

99.3%

Counts

884 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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)))))
▶	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (.f32 alpha alpha) (/.f32 #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 -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)))))
	-0.0%	(fma.f32 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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)))))
▶	-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))))
	98.2%	(/.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))))
	98.2%	(/.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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (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))))) cosTheta) cosTheta))))
	86.2%	(/.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 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) cosTheta) cosTheta))))
	31.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (/.f32 (-.f32 (pow.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)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.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 (.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)))) (fma.f32 (/.f32 #s(literal 1 binary32) (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 (.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)))))))) cosTheta) cosTheta))))
	83.7%	(/.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 (.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))))) cosTheta) cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	95.4%	(/.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)) #s(literal 1 binary32))))
▶	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 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))))
	98.1%	(/.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))))
	7.1%	#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)))))
	70.3%	#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 1 742 to 740 computations (57.5% saved)

simplify11.0ms (0.1%)

Memory

-14.1MiB live, 24.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	522
0	84	520

Stop Event

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

Calls

Call 1

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

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

localize170.0ms (1.8%)

Memory

6.6MiB live, 429.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	100.0%	#s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)
✓	accuracy	100.0%	(.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	100.0%	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)

Samples

71.0ms

256×

invalid

Compiler

Compiled 548 to 44 computations (92% saved)

Precisions

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

ival-mult: 24.0ms (46.9% of total)

ival-div: 9.0ms (17.6% of total)

ival-add: 9.0ms (17.6% of total)

ival-log: 6.0ms (11.7% of total)

ival-pi: 1.0ms (2% of total)

ival-sub: 1.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series88.0ms (0.9%)

Memory

-13.7MiB live, 171.4MiB allocated

Counts

26 → 324

Calls

Call 1

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

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
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#<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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<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))))))))>
#<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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<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))))))))>
#<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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log (pow alpha 2)))) (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2)))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 3))) (* (PI) (log (pow alpha 2))))) (* -1 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))))) (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2)))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))))) (pow cosTheta 2))>
#<alt (* -1 alpha)>
#<alt (* alpha (- alpha 1))>
#<alt (* alpha (- alpha 1))>
#<alt (* alpha (- alpha 1))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt -1>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt alpha>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* 2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (+ 1 (* -1 (pow cosTheta 2)))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))>
#<alt 1>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>

Calls

105 calls:

Time	Variable		Point	Expression
22.0ms	alpha	@	0	(log alpha)
10.0ms	alpha	@	-inf	(* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
8.0ms	alpha	@	-inf	(log alpha)
4.0ms	alpha	@	inf	(log alpha)
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

simplify524.0ms (5.5%)

Memory

-3.3MiB live, 712.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 958×	`lower-*.f64`
6 958×	`lower-*.f32`
6 430×	`lower-fma.f64`
6 430×	`lower-fma.f32`
3 060×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	443	7780
1	1490	7530
2	6261	7424
0	8425	7034

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 322

Calls

Call 1

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

rewrite21.0ms (0.2%)

Memory

25.9MiB live, 25.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	294
0	84	292

Stop Event

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

Counts

26 → 29

Calls

Call 1

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

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

eval84.0ms (0.9%)

Memory: -6.0MiB live, 108.5MiB allocated
Compiler: Compiled 20 636 to 579 computations (97.2% saved)

prune121.0ms (1.3%)

Memory

-4.9MiB live, 157.5MiB allocated

Pruning

41 alts after pruning (39 fresh and 2 done)

	Pruned	Kept	Total
New	585	23	608
Fresh	1	16	17
Picked	3	2	5
Done	0	0	0
Total	589	41	630

Accuracy

99.4%

Counts

630 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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)))))
✓	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
▶	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
▶	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (.f32 alpha alpha) (/.f32 #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 -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)))))
	-0.0%	(fma.f32 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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)))))
▶	-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))))
	98.2%	(/.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))))
	98.2%	(/.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))))
✓	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))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	81.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (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))))) cosTheta) cosTheta))))
	86.2%	(/.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 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) cosTheta) cosTheta))))
	31.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (/.f32 (-.f32 (pow.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)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.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 (.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)))) (fma.f32 (/.f32 #s(literal 1 binary32) (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 (.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)))))))) cosTheta) cosTheta))))
	83.7%	(/.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 (.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))))) cosTheta) cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
▶	98.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) #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))))
	98.0%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 #s(approx (+ alpha -1) (+.f32 alpha (.f32 (/.f32 #s(literal -1 binary32) 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 (+.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))))
▶	98.1%	(/.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))))
	98.1%	(/.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 (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))))
	95.0%	(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
	69.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	7.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))))
	70.3%	#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 2 966 to 1 400 computations (52.8% saved)

simplify17.0ms (0.2%)

Memory

-17.4MiB live, 21.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

50×	`lower-*.f64`
44×	`lift-*.f32`
22×	`lower-+.f64`
18×	`lift-/.f32`
16×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	685
0	121	683

Stop Event

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

Calls

Call 1

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

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

localize297.0ms (3.1%)

Memory

29.5MiB live, 310.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	#s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)))
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	100.0%	#s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	100.0%	#s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	6.3%	(PI.f32)

Samples

136.0ms

256×

invalid

Compiler

Compiled 684 to 45 computations (93.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 23.0ms (47.9% of total)

ival-add: 9.0ms (18.8% of total)

ival-div: 7.0ms (14.6% of total)

ival-log: 5.0ms (10.4% of total)

ival-pi: 1.0ms (2.1% of total)

ival-sub: 1.0ms (2.1% of total)

exact: 1.0ms (2.1% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

series33.0ms (0.3%)

Memory

-6.4MiB live, 32.4MiB allocated

Counts

28 → 300

Calls

Call 1

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

Outputs
#<alt -1>
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#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
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#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
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#<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))))))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
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#<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))))))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<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))))))))>
#<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))))))))>
#<alt (- (+ (/ 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))))))>
#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log (pow alpha 2))))>
#<alt (- (+ (* -1 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
#<alt (- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log (pow alpha 2)))) (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2)))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
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#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
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#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ alpha (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ alpha (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ (* alpha (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (+ (/ alpha (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (+ (/ alpha (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (+ (/ (* alpha (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (/ (* alpha (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))))))))) (pow cosTheta 2))>
#<alt (* -1 alpha)>
#<alt (* alpha (- alpha 1))>
#<alt (* alpha (- alpha 1))>
#<alt (* alpha (- alpha 1))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
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#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- 1 (/ 1 alpha)))>
#<alt -1>
#<alt (- alpha 1)>
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#<alt (- alpha 1)>
#<alt alpha>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
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#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<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))))))))>
#<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))))))))>
#<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))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
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#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
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#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2))))>
#<alt (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1)))) (* (PI) (log (pow alpha 2))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2)))) (* (PI) (log (pow alpha 2)))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3)))) (* (PI) (log (pow alpha 2))))) (* -1 (/ (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log (pow alpha 2))))))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt 1>
#<alt (+ 1 alpha)>
#<alt (+ 1 alpha)>
#<alt (+ 1 alpha)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ 1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>
#<alt (* -2 (* (PI) (log (/ -1 alpha))))>

Calls

105 calls:

Time	Variable		Point	Expression
21.0ms	cosTheta	@	inf	(+ (* (/ 1 (PI)) (/ (* alpha alpha) (* (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (/ 0 0)))) (/ -1 (* (/ 0 0) (+ (* (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)))))
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))))
1.0ms	cosTheta	@	0	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
0.0ms	alpha	@	-inf	(* (+ alpha 1) (+ alpha -1))

simplify549.0ms (5.8%)

Memory

15.7MiB live, 409.3MiB allocated

Algorithm

1×	egg-herbie

Rules

5 260×	`lower-fma.f64`
5 260×	`lower-fma.f32`
4 934×	`lower-*.f64`
4 934×	`lower-*.f32`
3 188×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	301	5636
1	1013	5414
2	4431	5307
0	8258	5061

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 296

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

rewrite39.0ms (0.4%)

Memory

-33.8MiB live, 43.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

50×	`lower-*.f64`
44×	`lift-*.f32`
22×	`lower-+.f64`
18×	`lift-/.f32`
16×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	312
0	121	310

Stop Event

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

Counts

28 → 33

Calls

Call 1

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

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

eval38.0ms (0.4%)

Memory: 21.3MiB live, 66.7MiB allocated
Compiler: Compiled 18 058 to 371 computations (97.9% saved)

prune152.0ms (1.6%)

Memory

-14.5MiB live, 146.8MiB allocated

Pruning

44 alts after pruning (39 fresh and 5 done)

	Pruned	Kept	Total
New	479	5	484
Fresh	0	34	34
Picked	2	3	5
Done	0	2	2
Total	481	44	525

Accuracy

99.5%

Counts

525 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
▶	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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)))))
✓	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
✓	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
▶	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
✓	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (.f32 alpha alpha) (/.f32 #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 -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)))))
	-0.0%	(fma.f32 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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)))))
	98.2%	(/.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))))
▶	98.2%	(/.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))))
✓	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))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	81.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (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))))) cosTheta) cosTheta))))
	86.2%	(/.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 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) cosTheta) cosTheta))))
	31.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (/.f32 (-.f32 (pow.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)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.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 (.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)))) (fma.f32 (/.f32 #s(literal 1 binary32) (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 (.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)))))))) cosTheta) cosTheta))))
	83.7%	(/.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 (.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))))) cosTheta) cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 #s(approx (+ alpha -1) (+.f32 alpha (.f32 (/.f32 #s(literal -1 binary32) 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 (+.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))))
✓	98.1%	(/.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))))
▶	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.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 (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))))
	95.0%	(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
	69.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	97.9%	(/.f32 #s(approx (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.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))))
▶	-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))))
	7.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))))
	70.3%	#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 3 067 to 1 456 computations (52.5% saved)

simplify27.0ms (0.3%)

Memory

-9.9MiB live, 28.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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) #s(approx (log ( alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (PI.f32))
✓	cost-diff	0	(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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	64	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	0	(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
✓	cost-diff	0	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #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	(.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)))
✓	cost-diff	0	(+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (*.f32 alpha alpha))))
✓	cost-diff	0	(/.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)))))
✓	cost-diff	0	(/.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))))

Rules

48×	`lower-*.f64`
38×	`lift-*.f32`
22×	`lower-+.f64`
20×	`lift-/.f32`
20×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	731
0	120	731

Stop Event

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

Calls

Call 1

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

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

localize269.0ms (2.8%)

Memory

26.5MiB live, 379.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f32 #s(literal 2 binary32) (log.f32 alpha))
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	100.0%	#s(approx (log (* alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha)))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	accuracy	100.0%	(.f32 cosTheta (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	100.0%	#s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))
✓	accuracy	100.0%	#s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(neg.f32 (*.f32 alpha alpha))
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

122.0ms

256×

invalid

Compiler

Compiled 743 to 54 computations (92.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-mult: 38.0ms (44.6% of total)

ival-add: 22.0ms (25.8% of total)

ival-div: 10.0ms (11.7% of total)

ival-log: 9.0ms (10.6% of total)

ival-sub: 2.0ms (2.3% of total)

ival-neg: 2.0ms (2.3% of total)

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

exact: 1.0ms (1.2% of total)

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

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

series26.0ms (0.3%)

Memory

14.3MiB live, 52.0MiB allocated

Counts

31 → 348

Calls

Call 1

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

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (- (* 1/2 (/ (* (pow alpha 2) (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2)))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* -1 (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (+ (* -1 (/ (* (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))) (+ 1 (* -1 (pow cosTheta 2))))) (+ (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3))))))))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 3)))))))) (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (* -1 (/ (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (pow (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) 2) (* (pow cosTheta 6) (* (PI) (log (/ 1 alpha))))))) (pow alpha 4))) (+ (* -1/2 (/ (+ 1 (+ (* -1 (pow cosTheta 2)) (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
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#<alt (- (+ (/ 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))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (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 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))))>
#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2))))>
#<alt (+ (* -1 (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1)))) (* (PI) (log (pow alpha 2))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2)))) (* (PI) (log (pow alpha 2)))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3)))) (* (PI) (log (pow alpha 2))))) (* -1 (/ (* (+ 1 alpha) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log (pow alpha 2))))))) (/ (* (+ 1 alpha) (* (- alpha 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (log (pow alpha 2)))))>
#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))>
#<alt (/ (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))))) (/ (* (+ 1 alpha) (- alpha 1)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt 1>
#<alt (+ 1 alpha)>
#<alt (+ 1 alpha)>
#<alt (+ 1 alpha)>
#<alt alpha>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt (* alpha (+ 1 (/ 1 alpha)))>
#<alt -1>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt (- alpha 1)>
#<alt alpha>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt (* alpha (- 1 (/ 1 alpha)))>
#<alt alpha>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* -1 (* alpha (- (/ 1 alpha) 1)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (* -1 (pow alpha 2))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* -1 cosTheta)>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) cosTheta)>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* cosTheta (- (pow alpha 2) 1))>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* (pow cosTheta 2) (- (pow alpha 2) 1))>
#<alt (* -1 (pow cosTheta 2))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (pow cosTheta 2))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (pow cosTheta 2)))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>
#<alt (* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))>

Calls

111 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta	@	-inf	(/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify313.0ms (3.3%)

Memory

-12.4MiB live, 630.9MiB allocated

Algorithm

1×	egg-herbie

Rules

5 988×	`lower-*.f64`
5 988×	`lower-*.f32`
5 242×	`lower-fma.f64`
5 242×	`lower-fma.f32`
3 842×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	516	6795
1	1700	6282
2	7901	6224
0	8352	5943

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 343

Calls

Call 1

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

rewrite45.0ms (0.5%)

Memory

-7.0MiB live, 81.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

48×	`lower-*.f64`
38×	`lift-*.f32`
22×	`lower-+.f64`
20×	`lift-/.f32`
20×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	354
0	120	354

Stop Event

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

Counts

31 → 36

Calls

Call 1

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

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

eval50.0ms (0.5%)

Memory: -10.2MiB live, 141.3MiB allocated
Compiler: Compiled 24 793 to 600 computations (97.6% saved)

prune82.0ms (0.9%)

Memory

15.8MiB live, 213.9MiB allocated

Pruning

60 alts after pruning (50 fresh and 10 done)

	Pruned	Kept	Total
New	570	18	588
Fresh	2	32	34
Picked	0	5	5
Done	0	5	5
Total	572	60	632

Accuracy

99.5%

Counts

632 → 60

Alt Table

Click to see full alt table

Status	Accuracy	Program
	-0.0%	(fma.f32 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
✓	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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)))))
	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
	-0.0%	(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
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	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	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))))
✓	98.1%	(/.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))))
✓	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(approx (+ alpha -1) (+.f32 alpha (.f32 alpha (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.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 (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))))
	95.0%	(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
	69.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	97.9%	(/.f32 #s(approx (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.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))))
✓	-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))))
	70.3%	#s(approx (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))
	7.3%	#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 4 501 to 1 338 computations (70.3% saved)

regimes81.0ms (0.9%)

Memory

12.7MiB live, 209.5MiB allocated

Counts

69 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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 (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.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 #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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) 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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.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 (.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 #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 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) cosTheta) 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 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #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 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(approx (+ alpha -1) (+.f32 alpha (.f32 alpha (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.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 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 #s(approx (+ alpha -1) (+.f32 alpha (.f32 (/.f32 #s(literal -1 binary32) 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 (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) #s(literal -1 binary32)) (+.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))))
(/.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 (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))))) 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))))
(/.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 (.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))))) 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 (pow.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)))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) #s(literal 3 binary32))) (fma.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 (.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)))) (fma.f32 (/.f32 #s(literal 1 binary32) (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 (.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)))))))) 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))))

Calls

4 calls:

21.0ms	(/.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	(*.f32 alpha alpha)
19.0ms	alpha
19.0ms	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)

regimes95.0ms (1%)

Memory

-33.0MiB live, 139.3MiB allocated

Counts

51 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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 (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.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 #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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

45.0ms	cosTheta
17.0ms	(*.f32 alpha alpha)
16.0ms	(/.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))))
15.0ms	alpha

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes71.0ms (0.7%)

Memory

23.9MiB live, 103.2MiB 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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 (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))

Outputs

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

Calls

4 calls:

28.0ms	(/.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))))
15.0ms	alpha
13.0ms	(*.f32 alpha alpha)
13.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
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)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes59.0ms (0.6%)

Memory

-4.4MiB live, 116.5MiB allocated

Counts

47 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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 (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.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 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))

Calls

4 calls:

15.0ms	alpha
14.0ms	(/.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))))
14.0ms	(*.f32 alpha alpha)
12.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.4%	1	`cosTheta`
95.4%	1	`alpha`
95.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
95.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes53.0ms (0.6%)

Memory

-4.3MiB live, 112.2MiB allocated

Counts

44 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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 (/ (/ (+ -1 (* (* alpha alpha) (* (* alpha alpha) (* alpha alpha)))) (+ 1 (- (* (* alpha alpha) (* alpha alpha)) (neg (* alpha alpha))))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)))))

Outputs

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

Calls

4 calls:

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))))
13.0ms	cosTheta
13.0ms	(*.f32 alpha alpha)
12.0ms	alpha

Results

Accuracy	Segments	Branch
70.3%	1	`cosTheta`
70.3%	1	`alpha`
70.3%	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))))`
70.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes51.0ms (0.5%)

Memory

16.0MiB live, 96.9MiB allocated

Counts

43 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 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)))))

Outputs

#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)))))

Calls

4 calls:

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))))
13.0ms	alpha
11.0ms	cosTheta
11.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
70.3%	1	`cosTheta`
70.3%	1	`alpha`
70.3%	1	`(*.f32 alpha alpha)`
70.3%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes52.0ms (0.6%)

Memory

-35.4MiB live, 90.3MiB allocated

Counts

42 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 ( (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (log alpha) (+ (PI) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 #s(literal 1/2 binary32) (.f32 alpha alpha) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))))

Outputs

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

Calls

4 calls:

14.0ms	cosTheta
13.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
11.0ms	alpha
11.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
69.0%	1	`cosTheta`
69.0%	1	`alpha`
69.0%	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))))`
69.0%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes47.0ms (0.5%)

Memory

8.4MiB live, 86.0MiB allocated

Counts

39 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (.f32 cosTheta (.f32 cosTheta (.f32 alpha alpha))))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.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 -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 (.f32 alpha alpha) (/.f32 #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 -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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (PI.f32)) (/.f32 alpha (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (.f32 alpha (.f32 alpha cosTheta)))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (*.f32 alpha alpha)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ (* alpha alpha) -1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 alpha #s(literal 1 binary32)) (/.f32 alpha (.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 -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 (/.f32 (.f32 alpha alpha) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))

Outputs

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

Calls

4 calls:

12.0ms	(/.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
10.0ms	alpha
10.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
3.5%	1	`cosTheta`
3.5%	1	`alpha`
3.5%	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))))`
3.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes20.0ms (0.2%)

Memory

-0.8MiB live, 38.2MiB allocated

Counts

13 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))
(fma.f32 #s(approx (/ alpha (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (fma.f32 (.f32 alpha (.f32 cosTheta cosTheta)) (neg.f32 (fma.f32 alpha alpha #s(literal -1 binary32))) alpha)) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #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 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 (fma.f32 #s(approx (+ (* alpha alpha) -1) (.f32 alpha alpha)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (.f32 #s(approx (+ ( alpha alpha) -1) #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32)))))

Outputs

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

Calls

4 calls:

6.0ms	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	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes11.0ms (0.1%)

Memory

24.7MiB live, 24.7MiB allocated

Counts

6 → 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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 (/.f32 alpha (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 #s(approx ( cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32) (PI.f32)))))

Outputs

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

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

Results

Accuracy	Segments	Branch
3.2%	1	`alpha`
3.2%	1	`(*.f32 alpha alpha)`
3.2%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
3.2%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory

-14.8MiB live, 27.5MiB 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))))
(fma.f32 (/.f32 alpha #s(approx (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1) #s(literal 1 binary32))) (/.f32 alpha (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (/.f32 #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

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

Calls

4 calls:

4.0ms	cosTheta
2.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	(*.f32 alpha alpha)
2.0ms	alpha

Results

Accuracy	Segments	Branch
3.1%	1	`alpha`
3.1%	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))))`
3.1%	1	`(*.f32 alpha alpha)`
3.1%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory

-19.9MiB live, 19.1MiB 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:

4.0ms	alpha
2.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
2.0ms	(*.f32 alpha alpha)
2.0ms	cosTheta

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)

simplify28.0ms (0.3%)

Memory

19.5MiB live, 58.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	436
1	137	436
2	145	436
3	151	436

Stop Event

1×

saturated

Calls

Call 1

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

soundness1.1s (11.6%)

Memory

29.5MiB live, 972.9MiB allocated

Rules

8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
6 958×	`lower-*.f64`
6 958×	`lower-*.f32`
6 430×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	294
0	84	292
0	516	6795
1	1700	6282
2	7901	6224
0	8352	5943
0	301	5636
1	1013	5414
2	4431	5307
0	8258	5061
0	197	2350
1	582	2290
2	2231	2197
0	8730	2075
0	13	65
0	23	65
1	98	65
2	768	63
0	8446	55
0	443	7780
1	1490	7530
2	6261	7424
0	8425	7034

Stop Event

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

Compiler

Compiled 746 to 302 computations (59.5% saved)

preprocess105.0ms (1.1%)

Memory

-17.0MiB live, 267.9MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 1 624 to 706 computations (56.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze65.0ms (0.7%)

sample2.8s (29.4%)

preprocess364.0ms (3.8%)

explain172.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify323.0ms (3.4%)

localize40.0ms (0.4%)

series50.0ms (0.5%)

simplify348.0ms (3.7%)

rewrite365.0ms (3.8%)

eval87.0ms (0.9%)

prune136.0ms (1.4%)

simplify11.0ms (0.1%)

localize170.0ms (1.8%)

series88.0ms (0.9%)

simplify524.0ms (5.5%)

rewrite21.0ms (0.2%)

eval84.0ms (0.9%)

prune121.0ms (1.3%)

simplify17.0ms (0.2%)

localize297.0ms (3.1%)

series33.0ms (0.3%)

simplify549.0ms (5.8%)

rewrite39.0ms (0.4%)

eval38.0ms (0.4%)

prune152.0ms (1.6%)

simplify27.0ms (0.3%)

localize269.0ms (2.8%)

series26.0ms (0.3%)

simplify313.0ms (3.3%)

rewrite45.0ms (0.5%)

eval50.0ms (0.5%)

prune82.0ms (0.9%)

regimes81.0ms (0.9%)

regimes95.0ms (1%)

regimes71.0ms (0.7%)

regimes59.0ms (0.6%)

regimes53.0ms (0.6%)

regimes51.0ms (0.5%)

regimes52.0ms (0.6%)

regimes47.0ms (0.5%)

regimes20.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

simplify28.0ms (0.3%)

soundness1.1s (11.6%)

preprocess105.0ms (1.1%)

end0.0ms (0%)

Profiling