Metrics for GTR1 distribution

analyze54.0ms (0.5%)

Memory

19.5MiB live, 97.0MiB 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)

sample2.4s (24.7%)

Memory

12.7MiB live, 2 221.5MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 939.0ms

ival-mult: 277.0ms (29.5% of total)

const: 186.0ms (19.8% of total)

ival-log: 101.0ms (10.8% of total)

ival-<=: 97.0ms (10.3% of total)

ival-div: 81.0ms (8.6% of total)

ival-add: 80.0ms (8.5% of total)

ival-sub: 50.0ms (5.3% of total)

ival-pi: 29.0ms (3.1% of total)

ival-and: 24.0ms (2.6% of total)

exact: 10.0ms (1.1% of total)

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

Bogosity

preprocess1.3s (13.4%)

Memory

-6.7MiB live, 478.1MiB 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)

explain949.0ms (9.6%)

Memory

33.2MiB live, 377.8MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

548.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 268.0ms

ival-sub: 238.0ms (88.7% of total)

ival-mult: 16.0ms (6% of total)

ival-log: 6.0ms (2.2% of total)

ival-div: 4.0ms (1.5% of total)

ival-pi: 2.0ms (0.7% of total)

ival-add: 2.0ms (0.7% 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.6%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify360.0ms (3.7%)

Memory

-28.5MiB live, 602.8MiB 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

localize68.0ms (0.7%)

Memory

-31.9MiB live, 87.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(.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	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

52.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 36.0ms (82.5% of total)

ival-log: 3.0ms (6.9% of total)

ival-div: 2.0ms (4.6% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series67.0ms (0.7%)

Memory

6.1MiB live, 138.8MiB 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
45.0ms	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))))

simplify340.0ms (3.4%)

Memory

-2.0MiB live, 630.8MiB 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))

rewrite385.0ms (3.9%)

Memory

23.0MiB live, 623.9MiB 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 (.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)))

eval84.0ms (0.9%)

Memory: 12.4MiB live, 200.7MiB allocated
Compiler: Compiled 33 380 to 2 790 computations (91.6% saved)

prune138.0ms (1.4%)

Memory

-19.9MiB live, 336.1MiB allocated

Pruning

30 alts after pruning (30 fresh and 0 done)

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

Accuracy

99.7%

Counts

884 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
▶	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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)))))))) (.f32 (.f32 (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 (pow.f32 (/.f32 (.f32 (.f32 alpha 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 alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (.f32 (.f32 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 (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 (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	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)))))
	94.7%	(/.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))))
	98.3%	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	97.5%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (neg.f32 (PI.f32)))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
	94.6%	#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)))))
	65.6%	#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 2 588 to 1 048 computations (59.5% saved)

simplify10.0ms (0.1%)

Memory

19.4MiB live, 19.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

28×	`lower-*.f64`
24×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-/.f64`
10×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	574
0	69	574

Stop Event

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

Calls

Call 1

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

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

localize193.0ms (2%)

Memory

-39.3MiB live, 252.3MiB 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 (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 (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 (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 (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)

Samples

116.0ms

256×

invalid

Compiler

Compiled 610 to 40 computations (93.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 33.0ms (54.1% of total)

ival-div: 10.0ms (16.4% of total)

ival-add: 9.0ms (14.7% of total)

ival-sub: 4.0ms (6.6% of total)

ival-log: 3.0ms (4.9% of total)

ival-pi: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series56.0ms (0.6%)

Memory

2.0MiB live, 120.6MiB allocated

Counts

23 → 324

Calls

Call 1

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

Calls

93 calls:

Time	Variable		Point	Expression
12.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))
5.0ms	alpha	@	inf	(/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/ (/ (- 1 (* (* alpha alpha) (* alpha alpha))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

simplify443.0ms (4.5%)

Memory

44.6MiB live, 851.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8 876×	`lower-fma.f64`
8 876×	`lower-fma.f32`
7 360×	`lower-*.f64`
7 360×	`lower-*.f32`
4 206×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	624	11368
1	2175	10843
0	8395	10259

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 324

Calls

Call 1

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

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

rewrite26.0ms (0.3%)

Memory

1.4MiB live, 79.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

28×	`lower-*.f64`
24×	`lift-*.f32`
16×	`lift-/.f32`
16×	`lower-/.f64`
10×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	321
0	69	321

Stop Event

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

Counts

23 → 24

Calls

Call 1

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

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

eval68.0ms (0.7%)

Memory: 6.5MiB live, 175.5MiB allocated
Compiler: Compiled 30 135 to 745 computations (97.5% saved)

prune66.0ms (0.7%)

Memory

4.2MiB live, 206.6MiB allocated

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	736	20	756
Fresh	17	8	25
Picked	5	0	5
Done	0	0	0
Total	758	28	786

Accuracy

99.9%

Counts

786 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))))
	98.5%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (neg.f32 (log.f32 alpha)) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))) (.f32 alpha alpha))))))
	97.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	50.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))))
	94.6%	(/.f32 (fma.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)))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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)))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	81.3%	(/.f32 (/.f32 #s(approx (- 1 (* (* alpha alpha) (* alpha alpha))) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	94.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	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))))
▶	98.6%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	94.1%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	65.6%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	95.9%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (-.f32 (-.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
	94.4%	#s(approx (/ (/ (- 1 (* (* alpha alpha) (* alpha alpha))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
	97.5%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))

Compiler

Compiled 2 034 to 894 computations (56% saved)

simplify12.0ms (0.1%)

Memory

-8.0MiB live, 31.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
✓	cost-diff	0	(/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32))))
✓	cost-diff	0	(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 alpha #s(literal -1 binary32))
✓	cost-diff	0	(fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (*.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)))
✓	cost-diff	0	(/.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))))
✓	cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32)))
✓	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))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
✓	cost-diff	64	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 #s(literal 0 binary32) #s(literal 0 binary32))
✓	cost-diff	0	(.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32)))
✓	cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)))
✓	cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
✓	cost-diff	288	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)

Rules

32×	`lower-*.f64`
26×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	520
0	89	520

Stop Event

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

Calls

Call 1

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

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

localize192.0ms (1.9%)

Memory

1.1MiB live, 405.1MiB 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 (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%	(neg.f32 cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.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)))
✓	accuracy	100.0%	(.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)))
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	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)

Samples

112.0ms

256×

invalid

Compiler

Compiled 561 to 43 computations (92.3% saved)

Precisions

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

ival-mult: 41.0ms (46.6% of total)

ival-log: 25.0ms (28.4% of total)

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

ival-div: 7.0ms (8% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series48.0ms (0.5%)

Memory

-19.8MiB live, 58.8MiB allocated

Counts

22 → 312

Calls

Call 1

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

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

Calls

90 calls:

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

simplify370.0ms (3.8%)

Memory

10.8MiB live, 766.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 818×	`lower-*.f64`
5 818×	`lower-*.f32`
5 096×	`lower-fma.f64`
5 096×	`lower-fma.f32`
3 364×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	10238
1	1540	9802
2	7038	9788
0	8051	9337

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 310

Calls

Call 1

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

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

rewrite23.0ms (0.2%)

Memory

16.7MiB live, 55.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

32×	`lower-*.f64`
26×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lift-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	269
0	89	269

Stop Event

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

Counts

22 → 26

Calls

Call 1

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

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

eval48.0ms (0.5%)

Memory: -9.8MiB live, 144.7MiB allocated
Compiler: Compiled 20 937 to 599 computations (97.1% saved)

prune58.0ms (0.6%)

Memory

-22.3MiB live, 151.1MiB allocated

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	550	14	564
Fresh	7	16	23
Picked	4	1	5
Done	0	0	0
Total	561	31	592

Accuracy

100.0%

Counts

592 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	97.3%	(/.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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 #s(approx (+ alpha -1) (neg.f32 (fma.f32 alpha (/.f32 #s(literal 1 binary32) alpha) (neg.f32 alpha)))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.3%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))))
	97.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	50.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))))
	94.6%	(/.f32 (fma.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)))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	76.0%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))))))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.0%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	94.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	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))))
✓	98.6%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	97.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	98.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (neg.f32 (.f32 cosTheta (.f32 cosTheta (*.f32 (PI.f32) (log.f32 alpha)))))))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 #s(literal 2 binary32) (PI.f32)))))
	97.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
▶	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
	94.1%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	65.6%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	94.4%	#s(approx (/ (/ (- 1 (* (* alpha alpha) (* alpha alpha))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
	96.1%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))) (/.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	94.0%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
	65.6%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))

Compiler

Compiled 1 735 to 953 computations (45.1% saved)

simplify11.0ms (0.1%)

Memory

31.2MiB live, 31.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (*.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32))))
✓	cost-diff	0	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	192	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	256	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(+.f32 alpha #s(literal 1 binary32))
✓	cost-diff	0	(fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32))))
✓	cost-diff	0	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	256	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32)))
✓	cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
✓	cost-diff	192	(fma.f32 alpha alpha #s(literal -1 binary32))
✓	cost-diff	0	(fma.f32 (.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 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	(/.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	(PI.f32)
✓	cost-diff	0	(fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))
✓	cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))))
✓	cost-diff	192	(fma.f32 alpha alpha #s(literal -1 binary32))

Rules

38×	`lower-*.f64`
26×	`lift-*.f32`
18×	`lower-+.f64`
14×	`lift-/.f32`
14×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	549
0	108	546

Stop Event

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

Calls

Call 1

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

localize192.0ms (2%)

Memory

7.8MiB live, 315.5MiB 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%	(neg.f32 (+.f32 alpha #s(literal 1 binary32)))
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.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)))
✓	accuracy	100.0%	(.f32 cosTheta #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)))
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

94.0ms

256×

invalid

Compiler

Compiled 586 to 48 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 30.0ms (52.6% of total)

ival-add: 10.0ms (17.5% of total)

ival-div: 9.0ms (15.8% of total)

ival-log: 3.0ms (5.3% of total)

ival-sub: 2.0ms (3.5% of total)

ival-neg: 2.0ms (3.5% of total)

ival-pi: 1.0ms (1.8% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.2%)

Memory

2.5MiB live, 40.1MiB allocated

Counts

23 → 324

Calls

Call 1

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

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

Calls

93 calls:

Time	Variable		Point	Expression
3.0ms	cosTheta	@	inf	(+ (* (PI) (log (* alpha alpha))) (* (* cosTheta cosTheta) (* (log (* alpha alpha)) (* (PI) (+ (* alpha alpha) -1)))))
1.0ms	cosTheta	@	inf	(/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	0	(+ (* (PI) (log (* alpha alpha))) (* (* cosTheta cosTheta) (* (log (* alpha alpha)) (* (PI) (+ (* alpha alpha) -1)))))
1.0ms	cosTheta	@	0	(+ (* (PI) (log (* alpha alpha))) (* (* cosTheta cosTheta) (* (log (* alpha alpha)) (* (PI) (+ (* alpha alpha) -1)))))

simplify373.0ms (3.8%)

Memory

-0.7MiB live, 588.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 980×	`lower-*.f64`
5 980×	`lower-*.f32`
5 956×	`lower-fma.f64`
5 956×	`lower-fma.f32`
3 388×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	467	10426
1	1557	9996
2	7089	9936
0	8075	9458

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 322

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

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

rewrite24.0ms (0.2%)

Memory

-0.4MiB live, 37.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	276
0	108	274

Stop Event

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

Counts

23 → 29

Calls

Call 1

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

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

eval39.0ms (0.4%)

Memory: -10.2MiB live, 65.8MiB allocated
Compiler: Compiled 16 873 to 513 computations (97% saved)

prune86.0ms (0.9%)

Memory

38.3MiB live, 113.5MiB allocated

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	434	9	443
Fresh	4	21	25
Picked	3	2	5
Done	0	1	1
Total	441	33	474

Accuracy

100.0%

Counts

474 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
	97.3%	(/.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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 #s(approx (+ alpha -1) (neg.f32 (fma.f32 alpha (/.f32 #s(literal 1 binary32) alpha) (neg.f32 alpha)))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
	65.7%	(/.f32 (fma.f32 alpha #s(approx (+ alpha 1) #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))))
✓	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))))
	97.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	50.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))))
	94.6%	(/.f32 (fma.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)))))
	98.3%	(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	75.9%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
	97.5%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))))))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.0%	(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
	94.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	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))))
✓	98.6%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
✓	97.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (/.f32 (neg.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha)) (neg.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
	97.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 #s(literal 2 binary32) (PI.f32)))))
	97.0%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
	-0.0%	(/.f32 #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) #s(approx (+ ( (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)) (PI.f32))))
	94.1%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
	65.6%	#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	94.4%	#s(approx (/ (/ (- 1 (* (* alpha alpha) (* alpha alpha))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
	96.1%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))) (/.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	94.1%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
	65.6%	#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (-.f32 (PI.f32) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	94.3%	#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (fma.f32 alpha alpha alpha) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

Compiler

Compiled 3 347 to 813 computations (75.7% saved)

regimes123.0ms (1.3%)

Memory

-14.9MiB live, 115.7MiB allocated

Counts

74 → 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)) #s(approx (+ ( (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)) (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))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (fma.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 (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (-.f32 (PI.f32) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (fma.f32 alpha alpha alpha) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 #s(literal 2 binary32) (PI.f32)))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (fma.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
#s(approx (/ (/ (- 1 (* (* alpha alpha) (* alpha alpha))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.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 #s(approx (- (* alpha alpha) 1) #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 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (fma.f32 alpha #s(approx (+ alpha 1) #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha (+.f32 alpha #s(literal 1 binary32)) (neg.f32 (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (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 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))))
(/.f32 (/.f32 #s(approx (- 1 (* (* alpha alpha) (* alpha alpha))) #s(literal 1 binary32)) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(approx (+ (* alpha alpha) -1) #s(literal -1 binary32))) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (*.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))))
(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 #s(approx (+ alpha -1) (neg.f32 (fma.f32 alpha (/.f32 #s(literal 1 binary32) alpha) (neg.f32 alpha)))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.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 (fma.f32 (.f32 alpha alpha) (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (/.f32 (.f32 (.f32 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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (fma.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (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)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (fma.f32 (PI.f32) (log.f32 (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal -1 binary32))))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (neg.f32 (log.f32 alpha)) (.f32 alpha alpha))) (neg.f32 (.f32 cosTheta (.f32 cosTheta (*.f32 (PI.f32) (log.f32 alpha)))))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (/.f32 (neg.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha)) (neg.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (PI.f32) (.f32 (neg.f32 (log.f32 alpha)) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))) (.f32 alpha alpha))))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (/.f32 (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha))))) (/.f32 (.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (fma.f32 alpha (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)))))))
(/.f32 (/.f32 (.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 (fma.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (fma.f32 alpha (.f32 alpha (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 alpha alpha) (fma.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (neg.f32 (PI.f32)))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1))) (fma.f32 (.f32 cosTheta cosTheta) (fma.f32 (.f32 cosTheta cosTheta) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (neg.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (-.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))))))) (.f32 (fma.f32 alpha alpha (-.f32 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 alpha 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 alpha #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (fma.f32 alpha alpha #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (/.f32 (.f32 (.f32 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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (-.f32 (-.f32 (fma.f32 (neg.f32 (.f32 cosTheta cosTheta)) (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (fma.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (fma.f32 alpha alpha #s(literal 1 binary32)) (neg.f32 (fma.f32 alpha alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32)))))))
(/.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)))))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

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

Calls

4 calls:

51.0ms	(/.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))))
27.0ms	cosTheta
19.0ms	(*.f32 alpha alpha)
18.0ms	alpha

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta`
98.7%	1	`alpha`
98.7%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes32.0ms (0.3%)

Memory

-16.3MiB live, 58.7MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

9.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta
7.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms	alpha

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`alpha`
98.6%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes29.0ms (0.3%)

Memory

10.6MiB live, 57.1MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

10.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
6.0ms	alpha
6.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.5%	1	`alpha`
97.5%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes26.0ms (0.3%)

Memory

14.5MiB live, 51.2MiB allocated

Counts

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

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:

8.0ms	cosTheta
6.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms	(*.f32 alpha alpha)
5.0ms	alpha

Results

Accuracy	Segments	Branch
97.5%	1	`alpha`
97.5%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes26.0ms (0.3%)

Memory

-23.2MiB live, 51.4MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

7.0ms	alpha
5.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
5.0ms	(*.f32 alpha alpha)
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.5%	1	`alpha`
97.5%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes23.0ms (0.2%)

Memory

10.9MiB live, 54.4MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

8.0ms	alpha
5.0ms	(/.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
97.4%	1	`cosTheta`
97.4%	1	`alpha`
97.4%	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))))`
97.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes19.0ms (0.2%)

Memory

5.3MiB live, 42.9MiB 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)) #s(approx (+ ( (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)) (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))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta #s(approx (* (+ (* alpha alpha) -1) cosTheta) (neg.f32 cosTheta))) (PI.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)) (fma.f32 (.f32 cosTheta (*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta)) (PI.f32) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (fma.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 (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (-.f32 (PI.f32) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
#s(approx (/ (/ (- (* (* (* alpha alpha) (* alpha alpha)) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 #s(literal -1/2 binary32) (.f32 (fma.f32 cosTheta (neg.f32 cosTheta) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* (+ (* alpha alpha) -1) cosTheta) cosTheta) 1)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
#s(approx (/ (+ (* alpha (+ alpha 1)) (neg (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (+.f32 (fma.f32 alpha alpha alpha) (-.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

6.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
4.0ms	(*.f32 alpha alpha)
4.0ms	cosTheta
4.0ms	alpha

Results

Accuracy	Segments	Branch
94.7%	1	`cosTheta`
94.7%	1	`alpha`
94.7%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
94.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes16.0ms (0.2%)

Memory

-1.9MiB live, 35.9MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

5.0ms	(*.f32 alpha alpha)
4.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
3.0ms	cosTheta
3.0ms	alpha

Results

Accuracy	Segments	Branch
94.6%	1	`alpha`
94.6%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
94.6%	1	`(*.f32 alpha alpha)`
94.6%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes10.0ms (0.1%)

Memory

-14.5MiB live, 23.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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)) #s(approx (+ ( (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)) (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))))
(/.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)) #s(approx (+ (* (* cosTheta (* (+ (* alpha alpha) -1) cosTheta)) (PI)) (PI)) (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	cosTheta
2.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
-0.0%	1	`cosTheta`
-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)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

simplify9.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary32`
10×	`sub-neg_binary32`
10×	`+-commutative_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	276
1	88	276
2	97	276
3	105	276
4	106	276

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

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

soundness919.0ms (9.3%)

Memory

-6.3MiB live, 998.0MiB allocated

Rules

8 876×	`lower-fma.f64`
8 876×	`lower-fma.f32`
8 466×	`lower-fma.f64`
8 466×	`lower-fma.f32`
7 360×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	10238
1	1540	9802
2	7038	9788
0	8051	9337
0	467	10426
1	1557	9996
2	7089	9936
0	8075	9458
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	624	11368
1	2175	10843
0	8395	10259

Stop Event

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

Compiler

Compiled 598 to 273 computations (54.3% saved)

preprocess50.0ms (0.5%)

Memory

16.6MiB live, 131.7MiB allocated

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 916 to 442 computations (51.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze54.0ms (0.5%)

sample2.4s (24.7%)

preprocess1.3s (13.4%)

explain949.0ms (9.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify360.0ms (3.7%)

localize68.0ms (0.7%)

series67.0ms (0.7%)

simplify340.0ms (3.4%)

rewrite385.0ms (3.9%)

eval84.0ms (0.9%)

prune138.0ms (1.4%)

simplify10.0ms (0.1%)

localize193.0ms (2%)

series56.0ms (0.6%)

simplify443.0ms (4.5%)

rewrite26.0ms (0.3%)

eval68.0ms (0.7%)

prune66.0ms (0.7%)

simplify12.0ms (0.1%)

localize192.0ms (1.9%)

series48.0ms (0.5%)

simplify370.0ms (3.8%)

rewrite23.0ms (0.2%)

eval48.0ms (0.5%)

prune58.0ms (0.6%)

simplify11.0ms (0.1%)

localize192.0ms (2%)

series22.0ms (0.2%)

simplify373.0ms (3.8%)

rewrite24.0ms (0.2%)

eval39.0ms (0.4%)

prune86.0ms (0.9%)

regimes123.0ms (1.3%)

regimes32.0ms (0.3%)

regimes29.0ms (0.3%)

regimes26.0ms (0.3%)

regimes26.0ms (0.3%)

regimes23.0ms (0.2%)

regimes19.0ms (0.2%)

regimes16.0ms (0.2%)

regimes10.0ms (0.1%)

simplify9.0ms (0.1%)

soundness919.0ms (9.3%)

preprocess50.0ms (0.5%)

end0.0ms (0%)

Profiling