Metrics for GTR1 distribution

analyze58.0ms (0.7%)

Memory

20.0MiB live, 95.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 40 to 23 computations (42.5% saved)

sample1.7s (20.5%)

Memory

-92.6MiB live, 2 510.9MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 904.0ms

ival-mult: 322.0ms (35.6% of total)

ival-log: 142.0ms (15.7% of total)

const: 116.0ms (12.8% of total)

ival-<=: 104.0ms (11.5% of total)

ival-div: 80.0ms (8.8% of total)

ival-sub: 38.0ms (4.2% of total)

ival-add: 37.0ms (4.1% of total)

ival-pi: 28.0ms (3.1% of total)

ival-and: 23.0ms (2.5% of total)

exact: 11.0ms (1.2% of total)

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

Bogosity

preprocess483.0ms (5.7%)

Memory

-9.6MiB live, 667.0MiB allocated

Algorithm

2×	egg-herbie

Rules

12 798×	`accelerator-lowering-fma.f32`
12 798×	`accelerator-lowering-fma.f64`
4 578×	`-lowering-.f32`
4 578×	`-lowering-.f64`
2 370×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	150
1	166	146
2	648	144
3	3587	144
4	7869	144
0	13	24
1	41	24
2	149	24
3	628	24
4	2696	24
5	4449	24
6	7748	24
0	8594	21

Stop Event

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

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

Outputs

(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

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

Call 2

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))

Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(neg (/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta)))))
(/ (+ (* alpha alpha) -1) (* (* (PI) (log (* alpha alpha))) (+ -1 (* cosTheta (- cosTheta (* alpha (* alpha cosTheta)))))))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))
(/ (+ (* cosTheta cosTheta) -1) (* (log (* cosTheta cosTheta)) (+ (PI) (* (+ (* cosTheta cosTheta) -1) (* (* alpha alpha) (PI))))))

Symmetry

(abs cosTheta)

(abs alpha)

explain214.0ms (2.5%)

Memory

21.1MiB live, 341.6MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	2	254

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

85.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 51.0ms (73.6% of total)

ival-log: 8.0ms (11.6% of total)

ival-div: 4.0ms (5.8% of total)

ival-pi: 2.0ms (2.9% of total)

ival-add: 2.0ms (2.9% of total)

ival-sub: 2.0ms (2.9% 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: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

3.3MiB live, 3.3MiB 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)

simplify383.0ms (4.5%)

Memory

-35.7MiB live, 551.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	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	(*.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))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Rules

12 798×	`accelerator-lowering-fma.f32`
12 798×	`accelerator-lowering-fma.f64`
4 578×	`-lowering-.f32`
4 578×	`-lowering-.f64`
2 370×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
1	41	91
2	149	91
3	628	91
4	2696	91
5	4449	91
6	7748	91
0	8594	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
cosTheta

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

localize41.0ms (0.5%)

Memory

-4.3MiB live, 72.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.3%	(.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	98.9%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

25.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

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

ival-mult: 9.0ms (52.9% of total)

ival-log: 3.0ms (17.6% of total)

ival-div: 2.0ms (11.8% of total)

ival-pi: 1.0ms (5.9% of total)

ival-add: 1.0ms (5.9% of total)

ival-sub: 1.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

series62.0ms (0.7%)

Memory

-7.8MiB live, 109.3MiB allocated

Counts

7 → 132

Calls

Call 1

Inputs
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (- (* alpha alpha) 1)>
#<alt (* alpha alpha)>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (* (- (* alpha alpha) 1) cosTheta)>
#<alt (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)>

Outputs
#<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 -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow 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) (+ 1 (* -1 (pow cosTheta 2))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 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)) (+ 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 (* (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 (* -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)) (+ 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 (* (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)))>
#<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 (* 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
21.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
10.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
8.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
4.0ms	alpha	@	inf	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite476.0ms (5.6%)

Memory

31.2MiB live, 857.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 278×	`-lowering-.f32`
6 278×	`-lowering-.f64`
5 746×	`accelerator-lowering-fma.f32`
5 746×	`accelerator-lowering-fma.f64`
3 952×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	72
1	88	72
2	758	69
0	8431	61

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 762

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(- (* alpha alpha) 1)
(* alpha alpha)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(* (- (* alpha alpha) 1) cosTheta)
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)

Outputs
(neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))))
(neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))))
(neg.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(exp.f32 (.f32 (log.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))))) #s(literal -1 binary32)))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
(+.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
(+.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 alpha alpha)) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal -1 binary32)))
(+.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) #s(literal -1 binary32)) (.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (*.f32 alpha alpha)))
(+.f32 (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta))))) #s(literal 1 binary32)) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta))))) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32)))))
(+.f32 (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta))))) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) #s(literal -1 binary32)))) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (*.f32 cosTheta cosTheta))))) #s(literal 1 binary32)))
(+.f32 (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta))))) #s(literal 1 binary32)) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta))))) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(+.f32 (.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))) #s(literal 1 binary32)))
(+.f32 (.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)))))) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (*.f32 cosTheta cosTheta)))))))
(+.f32 (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) #s(literal -1 binary32))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)))))) (.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (*.f32 cosTheta cosTheta)))))))
(+.f32 (.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)))))) (.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (*.f32 cosTheta cosTheta)))))))
(pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))) #s(literal -1 binary32))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
(fma.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
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(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 cosTheta (+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) cosTheta)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) cosTheta)))
(/.f32 cosTheta (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
(/.f32 (.f32 cosTheta (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))
(/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(/.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) cosTheta) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))
(/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) cosTheta) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 cosTheta (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)))) (neg.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 cosTheta (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)))) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
(/.f32 (neg.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) cosTheta)) (neg.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) cosTheta)) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (*.f32 alpha alpha))))
(/.f32 (+.f32 (pow.f32 (.f32 cosTheta (.f32 alpha alpha)) #s(literal 3 binary32)) (pow.f32 (.f32 cosTheta #s(literal -1 binary32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha))) (-.f32 (.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta #s(literal -1 binary32))) (.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32))))))
(/.f32 (+.f32 (pow.f32 (.f32 (.f32 alpha alpha) cosTheta) #s(literal 3 binary32)) (pow.f32 (neg.f32 cosTheta) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta)) (-.f32 (.f32 (neg.f32 cosTheta) (neg.f32 cosTheta)) (.f32 (.f32 (*.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))))
(/.f32 (-.f32 (.f32 (.f32 cosTheta (.f32 alpha alpha)) (.f32 cosTheta (.f32 alpha alpha))) (.f32 (.f32 cosTheta #s(literal -1 binary32)) (.f32 cosTheta #s(literal -1 binary32)))) (-.f32 (.f32 cosTheta (.f32 alpha alpha)) (*.f32 cosTheta #s(literal -1 binary32))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) (.f32 (.f32 alpha alpha) cosTheta)) (.f32 (neg.f32 cosTheta) (neg.f32 cosTheta))) (-.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta)))
(.f32 #s(literal 1 binary32) (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 cosTheta #s(literal 1 binary32)))
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(.f32 (+.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 cosTheta (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(.f32 (.f32 cosTheta (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))
(.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))
(.f32 (/.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 (+.f32 (.f32 alpha (.f32 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) (*.f32 cosTheta (+.f32 alpha #s(literal 1 binary32)))) (+.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 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(/.f32 (.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
(/.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))
(/.f32 (neg.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (neg.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (.f32 alpha alpha))))
(.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta 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) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
(.f32 (.f32 cosTheta (+.f32 alpha #s(literal 1 binary32))) (*.f32 (+.f32 alpha #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))
(.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (.f32 alpha 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 cosTheta (*.f32 cosTheta (+.f32 alpha #s(literal 1 binary32)))) (+.f32 alpha #s(literal -1 binary32)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))
(.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (*.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 (*.f32 cosTheta cosTheta) (+.f32 alpha #s(literal -1 binary32))) (+.f32 alpha #s(literal 1 binary32)))

simplify440.0ms (5.2%)

Memory

10.5MiB live, 637.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 414×	`accelerator-lowering-fma.f32`
9 414×	`accelerator-lowering-fma.f64`
6 606×	`-lowering-.f32`
6 606×	`-lowering-.f64`
3 210×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	213	2672
1	663	2597
2	2605	2449
0	8225	2336

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log (pow alpha 2))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log (pow alpha 2))))))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* (pow cosTheta 2) (+ (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))) (/ (* (PI) (log (pow alpha 2))) (pow cosTheta 2))))
(* 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
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.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))))))))
(+.f32 (.f32 alpha (.f32 alpha (+.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (.f32 alpha alpha) (.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 (.f32 alpha (.f32 alpha (pow.f32 cosTheta #s(literal 4 binary32)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
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(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (+.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 alpha alpha)) (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32)))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(+.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.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 (+.f32 (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 alpha alpha)) (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (+.f32 (/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (+.f32 (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32)))))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (+.f32 (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.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 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (+.f32 (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log (pow alpha 2))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(-.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log (pow alpha 2)))) (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
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(.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 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))

eval95.0ms (1.1%)

Memory: 22.7MiB live, 209.9MiB allocated
Compiler: Compiled 40 972 to 3 131 computations (92.4% saved)

prune220.0ms (2.6%)

Memory

4.1MiB live, 370.7MiB allocated

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	1 014	22	1 036
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 014	23	1 037

Accuracy

99.8%

Counts

1 037 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.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))))
	98.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 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))))
▶	-0.0%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
	96.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.0%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.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))))
▶	97.9%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.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))))
	66.9%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.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))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
▶	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	46.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	98.4%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.1%	(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal -1 binary32) (neg.f32 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 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.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))))
	98.3%	(/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.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))))
	98.2%	(/.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))))
	98.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	98.4%	(+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal -1 binary32) (log.f32 (.f32 alpha alpha))) (-.f32 (.f32 (pow.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal 4 binary32)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32))))) (.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))))))

Compiler

Compiled 1 526 to 765 computations (49.9% saved)

simplify11.0ms (0.1%)

Memory

-8.6MiB live, 29.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
20×	`+-lowering-+.f64`
20×	`+-lowering-+.f32`
16×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	561

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))
(* (+ alpha -1) alpha)
(+ alpha -1)
alpha
-1
(* (+ alpha -1) 1)
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) (- 1 (* alpha alpha)))))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
1
(* alpha alpha)
alpha
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* (* cosTheta cosTheta) (- 1 (* alpha alpha))))
-1
(* (* cosTheta cosTheta) (- 1 (* alpha alpha)))
(* cosTheta cosTheta)
cosTheta
(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
(* (log alpha) (- 1 (* cosTheta cosTheta)))
(log alpha)
(- 1 (* cosTheta cosTheta))
(* cosTheta cosTheta)
cosTheta
(* (PI) 2)
(PI)
2
(/ (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* alpha (+ alpha 1)) (+ -1 (neg alpha)))
(* alpha (+ alpha 1))
alpha
(+ alpha 1)
1
(+ -1 (neg alpha))
-1
(neg alpha)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))
(* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1))
(+ (* alpha (* alpha alpha)) -1)
(* alpha (* alpha alpha))
alpha
(* alpha alpha)
-1
(+ (* alpha alpha) -1)
(* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))
(+ (* alpha alpha) (+ alpha 1))
(+ alpha 1)
1
(+ alpha -1)
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta

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

localize355.0ms (4.2%)

Memory

-16.1MiB live, 427.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f32 alpha (.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 alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.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)

Samples

110.0ms

256×

invalid

Compiler

Compiled 579 to 50 computations (91.4% saved)

Precisions

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

ival-mult: 51.0ms (59.8% of total)

ival-div: 12.0ms (14.1% of total)

ival-add: 11.0ms (12.9% of total)

ival-log: 6.0ms (7% of total)

ival-sub: 3.0ms (3.5% of total)

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

exact: 1.0ms (1.2% of total)

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

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

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

series141.0ms (1.7%)

Memory

-5.1MiB live, 146.0MiB allocated

Counts

27 → 336

Calls

Call 1

Inputs
#<alt (/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))>
#<alt (* (+ alpha -1) alpha)>
#<alt (+ alpha -1)>
#<alt (/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) (- 1 (* alpha alpha)))))>
#<alt (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))>
#<alt (- 1 (* alpha alpha))>
#<alt (* alpha alpha)>
#<alt (/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))>
#<alt (- (* alpha alpha) 1)>
#<alt (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))>
#<alt (/ (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha)))>
#<alt (* alpha (+ alpha 1))>
#<alt (+ alpha 1)>
#<alt (/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))>
#<alt (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1))>
#<alt (+ (* alpha (* alpha alpha)) -1)>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (* cosTheta cosTheta)>
#<alt (* (PI) (/ 0 0))>
#<alt (log alpha)>
#<alt (neg alpha)>
#<alt (* alpha (* alpha alpha))>

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

Calls

93 calls:

Time	Variable		Point	Expression
27.0ms	cosTheta	@	inf	(/ (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
27.0ms	alpha	@	-inf	(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
22.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
5.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
5.0ms	alpha	@	inf	(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))

rewrite16.0ms (0.2%)

Memory

29.9MiB live, 29.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
20×	`+-lowering-+.f64`
20×	`+-lowering-+.f32`
16×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	277

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

27 → 30

Calls

Call 1

Inputs
(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))
(* (+ alpha -1) alpha)
(+ alpha -1)
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) (- 1 (* alpha alpha)))))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
(* alpha alpha)
(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
(- (* alpha alpha) 1)
(* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2))
(/ (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(+ (* alpha (+ alpha 1)) (+ -1 (neg alpha)))
(* alpha (+ alpha 1))
(+ alpha 1)
(/ (/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))
(* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha alpha) -1))
(+ (* alpha (* alpha alpha)) -1)
(PI)
(log (* alpha alpha))
(* (PI) (log (* alpha alpha)))
(* cosTheta cosTheta)
(* (PI) (/ 0 0))
(log alpha)
(neg alpha)
(* alpha (* alpha alpha))

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

simplify707.0ms (8.3%)

Memory

-15.5MiB live, 624.0MiB allocated

Algorithm

1×	egg-herbie

Rules

5 774×	`accelerator-lowering-fma.f32`
5 774×	`accelerator-lowering-fma.f64`
5 760×	`-lowering-.f32`
5 760×	`-lowering-.f64`
3 954×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	495	9601
1	1649	9359
2	7342	9318
0	8239	8912

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

Outputs
(/ -1/2 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.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))))))))
(-.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (.f32 alpha (.f32 alpha (+.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (.f32 (.f32 alpha alpha) (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (.f32 alpha alpha) (-.f32 (.f32 (.f32 alpha alpha) (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.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)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (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 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (.f32 alpha alpha)))) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (.f32 alpha alpha)))) (+.f32 (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))))) (.f32 cosTheta (*.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32)))))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(+.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (.f32 alpha alpha)))) (+.f32 (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))))) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 alpha alpha)) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.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 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 alpha alpha)) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.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 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))
(+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 alpha alpha)) (-.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.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 (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (-.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 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 1/2 binary32)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32)))))))))
(/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log (pow alpha 2))))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1))) (* (PI) (log (pow alpha 2))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(+.f32 (neg.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log (pow alpha 2)))) (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2)))))) (+ (/ alpha (* (PI) (log (pow alpha 2)))) (/ (* alpha (- alpha 1)) (* (PI) (log (pow alpha 2)))))) (/ 1 (* (PI) (log (pow alpha 2)))))
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(/.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (+.f32 (/.f32 (/.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (/.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32))))))) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (+.f32 (/.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32)))))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))))))) (pow cosTheta 2))
(/.f32 (+.f32 (+.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32))))) (+.f32 (/.f32 (/.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32))) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))))) (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))) (pow.f32 cosTheta #s(literal 4 binary32))))) (+.f32 (+.f32 (/.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))))) (/.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32))) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))))))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))))))) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(- (pow alpha 2) 1)
(+.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(- (pow alpha 2) 1)
(+.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)))))
(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 (* -1 (pow alpha 2)))
(-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(+ 1 (* (pow alpha 2) (- (* -1 alpha) 1)))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))))
(+ 1 (* (pow alpha 2) (- (* alpha (- (pow alpha 2) 1)) 1)))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (.f32 alpha (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))))))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) alpha)) (.f32 alpha alpha))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha))) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (pow.f32 alpha #s(literal 5 binary32)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(neg.f32 (.f32 (pow.f32 alpha #s(literal 5 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))))))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(neg.f32 (.f32 (pow.f32 alpha #s(literal 5 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 alpha))))))
-1
#s(literal -1 binary32)
(- (pow alpha 3) 1)
(+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))
(- (pow alpha 3) 1)
(+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))
(- (pow alpha 3) 1)
(+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(.f32 (.f32 alpha alpha) (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(.f32 (.f32 alpha alpha) (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))))))
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(.f32 (.f32 alpha alpha) (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))))))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(.f32 (.f32 alpha (.f32 alpha alpha)) (neg.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(.f32 (.f32 alpha (.f32 alpha alpha)) (neg.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(.f32 (.f32 alpha (.f32 alpha alpha)) (neg.f32 (+.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha (*.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)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* 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 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #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)))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(* -1 alpha)
(neg.f32 alpha)
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))
(pow alpha 3)
(.f32 alpha (.f32 alpha alpha))

eval104.0ms (1.2%)

Memory: 4.0MiB live, 117.8MiB allocated
Compiler: Compiled 26 872 to 694 computations (97.4% saved)

prune90.0ms (1.1%)

Memory

-9.5MiB live, 113.5MiB allocated

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	651	18	669
Fresh	9	8	17
Picked	4	1	5
Done	0	1	1
Total	664	28	692

Accuracy

100.0%

Counts

692 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
▶	-0.0%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	84.5%	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (neg.f32 alpha)))) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
▶	96.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.7%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 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 alpha)))))) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.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))))
	66.9%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	66.9%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	96.2%	(/.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 #s(literal 2 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32)))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	97.8%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.1%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #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))))
	98.3%	(/.f32 (+.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #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))))
	96.6%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.9%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))))
▶	98.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	97.9%	(+.f32 (neg.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
	97.6%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
	97.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1 580 to 903 computations (42.8% saved)

simplify9.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`
18×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	463

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha))))
(* alpha alpha)
alpha
(+ 1 (/ -1 (* alpha alpha)))
1
(/ -1 (* alpha alpha))
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
1
(* alpha alpha)
alpha
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* (* cosTheta cosTheta) 1))
-1
(* (* cosTheta cosTheta) 1)
(* cosTheta cosTheta)
cosTheta
(/ (/ (+ -1 (* alpha alpha)) (PI)) (log (* alpha alpha)))
(/ (+ -1 (* alpha alpha)) (PI))
(+ -1 (* alpha alpha))
-1
(* alpha alpha)
alpha
(PI)
(log (* alpha alpha))
(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))
(* (+ alpha -1) alpha)
(+ alpha -1)
alpha
-1
(* (+ alpha -1) 1)
1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
(+ 1 (* (* -1 cosTheta) cosTheta))
(* (* -1 cosTheta) cosTheta)
(* -1 cosTheta)
cosTheta
(/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))
(- 1 (* alpha alpha))
1
(* alpha alpha)
alpha
(* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))
(+ (* alpha alpha) (+ alpha 1))
(+ alpha 1)
(+ alpha -1)
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta

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

localize247.0ms (2.9%)

Memory

3.3MiB live, 281.5MiB 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%	(*.f32 #s(literal -1 binary32) cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(+.f32 #s(literal -1 binary32) (*.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) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.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)

Samples

85.0ms

256×

invalid

Compiler

Compiled 471 to 45 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-mult: 34.0ms (53.1% of total)

ival-div: 14.0ms (21.9% of total)

ival-add: 9.0ms (14.1% of total)

ival-log: 3.0ms (4.7% of total)

ival-sub: 2.0ms (3.1% 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)

series41.0ms (0.5%)

Memory

8.1MiB live, 43.0MiB allocated

Counts

22 → 252

Calls

Call 1

Inputs
#<alt (/ (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha))))>
#<alt (* alpha alpha)>
#<alt (+ 1 (/ -1 (* alpha alpha)))>
#<alt (/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))>
#<alt (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))>
#<alt (- 1 (* alpha alpha))>
#<alt (/ (/ (+ -1 (* alpha alpha)) (PI)) (log (* alpha alpha)))>
#<alt (/ (+ -1 (* alpha alpha)) (PI))>
#<alt (+ -1 (* alpha alpha))>
#<alt (/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))>
#<alt (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))>
#<alt (* (+ alpha -1) alpha)>
#<alt (+ alpha -1)>
#<alt (/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (* cosTheta cosTheta)>
#<alt (* (PI) (/ 0 0))>
#<alt (* -1 cosTheta)>

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

Calls

72 calls:

Time	Variable		Point	Expression
19.0ms	alpha	@	inf	(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	inf	(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite34.0ms (0.4%)

Memory

-19.9MiB live, 19.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`
18×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	226

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

22 → 23

Calls

Call 1

Inputs
(/ (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha))))
(* alpha alpha)
(+ 1 (/ -1 (* alpha alpha)))
(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))
(/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0)))
(- 1 (* alpha alpha))
(/ (/ (+ -1 (* alpha alpha)) (PI)) (log (* alpha alpha)))
(/ (+ -1 (* alpha alpha)) (PI))
(+ -1 (* alpha alpha))
(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1))
(* (+ alpha -1) alpha)
(+ alpha -1)
(/ (/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (- 1 (* alpha alpha)) (* (+ (* alpha alpha) (+ alpha 1)) (+ alpha -1)))
(PI)
(log (* alpha alpha))
(* (PI) (log (* alpha alpha)))
(* cosTheta cosTheta)
(* (PI) (/ 0 0))
(* -1 cosTheta)

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

simplify489.0ms (5.8%)

Memory

4.4MiB live, 572.3MiB allocated

Algorithm

1×	egg-herbie

Rules

5 612×	`-lowering-.f32`
5 612×	`-lowering-.f64`
4 680×	`accelerator-lowering-fma.f32`
4 680×	`accelerator-lowering-fma.f64`
4 186×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	487	6692
1	1592	6388
2	6962	6365
0	8096	6128

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

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

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

eval41.0ms (0.5%)

Memory: -8.8MiB live, 109.5MiB allocated
Compiler: Compiled 17 606 to 567 computations (96.8% saved)

prune41.0ms (0.5%)

Memory

29.7MiB live, 106.5MiB allocated

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	512	14	526
Fresh	8	13	21
Picked	3	2	5
Done	0	2	2
Total	523	31	554

Accuracy

100.0%

Counts

554 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.6%	(/.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha))))
✓	77.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
	77.5%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	96.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.3%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.3%	(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 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 alpha)))))) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
▶	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.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%	(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	66.9%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	66.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))
	66.3%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	96.2%	(/.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 #s(literal 2 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32)))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.8%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.5%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #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 #s(literal -1 binary32) cosTheta) cosTheta))))
	96.6%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	77.7%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.3%	(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 alpha alpha) (PI.f32))) (log.f32 (.f32 alpha alpha)))
	95.9%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))))
	96.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.6%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
▶	66.8%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.5%	(+.f32 (+.f32 (/.f32 (/.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.1%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (*.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))))
	97.6%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
	97.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1 456 to 870 computations (40.2% saved)

simplify10.0ms (0.1%)

Memory

-20.2MiB live, 19.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`
12×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	426

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha)))))
(* (* alpha alpha) -2)
-2
(* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))
(- 0 (* (PI) (log alpha)))
0
(* (PI) (log alpha))
(PI)
(log alpha)
(+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha)))
(* cosTheta cosTheta)
cosTheta
(/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))
(- 1 (* cosTheta cosTheta))
(/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))
(/ 1 (* (PI) (/ 0 0)))
1
(* (PI) (/ 0 0))
(PI)
(/ 0 0)
0
(+ -1 (* (* cosTheta cosTheta) 1))
-1
(* (* cosTheta cosTheta) 1)
(* cosTheta cosTheta)
cosTheta
(/ -1 (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(* alpha alpha)
alpha
(+ 1 (* (* -1 cosTheta) cosTheta))
1
(* (* -1 cosTheta) cosTheta)
(* -1 cosTheta)
cosTheta
(/ (- (* alpha alpha) 1) (* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2))))
(- (* alpha alpha) 1)
(* alpha alpha)
alpha
1
(* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2)))
(* (PI) (log alpha))
(PI)
(log alpha)
(+ 2 (* (* cosTheta cosTheta) -2))
2
(* (* cosTheta cosTheta) -2)
(* cosTheta cosTheta)
cosTheta
-2
(/ (/ 1 (/ 1 (+ (* alpha alpha) -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ 1 (/ 1 (+ (* alpha alpha) -1)))
1
(/ 1 (+ (* alpha alpha) -1))
(+ (* alpha alpha) -1)
(* alpha alpha)
alpha
-1
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(PI)
(log (* alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(* (- (* alpha alpha) 1) cosTheta)
(- (* alpha alpha) 1)
cosTheta

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

localize167.0ms (2%)

Memory

-12.1MiB live, 279.1MiB 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 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(*.f32 #s(literal -1 binary32) cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32))
✓	accuracy	100.0%	(*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)

Samples

95.0ms

256×

invalid

Compiler

Compiled 436 to 48 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-mult: 41.0ms (56.2% of total)

ival-div: 14.0ms (19.2% of total)

ival-add: 7.0ms (9.6% of total)

ival-log: 6.0ms (8.2% of total)

ival-sub: 3.0ms (4.1% of total)

ival-pi: 1.0ms (1.4% of total)

exact: 1.0ms (1.4% of total)

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

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

series55.0ms (0.7%)

Memory

-0.8MiB live, 79.5MiB allocated

Counts

22 → 300

Calls

Call 1

Inputs
#<alt (/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))>
#<alt (- (* alpha alpha) 1)>
#<alt (* alpha alpha)>
#<alt (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha)))))>
#<alt (/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))>
#<alt (/ 1 (* (PI) (/ 0 0)))>
#<alt (* (PI) (/ 0 0))>
#<alt (PI)>
#<alt (/ -1 (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))>
#<alt (* (PI) (log (* alpha alpha)))>
#<alt (/ (- (* alpha alpha) 1) (* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2))))>
#<alt (* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2)))>
#<alt (/ (/ 1 (/ 1 (+ (* alpha alpha) -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ 1 (/ 1 (+ (* alpha alpha) -1)))>
#<alt (/ 1 (+ (* alpha alpha) -1))>
#<alt (+ (* alpha alpha) -1)>
#<alt (log alpha)>
#<alt (* cosTheta cosTheta)>
#<alt (* (* cosTheta cosTheta) 1)>
#<alt (log (* alpha alpha))>
#<alt (* -1 cosTheta)>

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))>
#<alt (- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (- 1 (pow cosTheta 2)) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (- (+ (* -1/2 (/ (* (- 1 (pow cosTheta 2)) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (- 1 (pow cosTheta 2)) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))>
#<alt (/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))>
#<alt (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))>
#<alt (- (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (- (+ (* -1/2 (/ (pow (- 1 (pow cosTheta 2)) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))>
#<alt (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))>
#<alt (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (* (- 1 (/ 1 (pow alpha 2))) (- (pow alpha 2) 1)))) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (- 1 (/ 1 (pow alpha 2))) (- (pow alpha 2) 1))) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (pow (- 1 (/ 1 (pow alpha 2))) 2) (- (pow alpha 2) 1)))) (* (PI) (log alpha)))))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (- 1 (/ 1 (pow alpha 2))) (- (pow alpha 2) 1))) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow alpha 6) (* (pow cosTheta 2) (* (pow (- 1 (/ 1 (pow alpha 2))) 3) (- (pow alpha 2) 1)))) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 4) (* (pow (- 1 (/ 1 (pow alpha 2))) 2) (- (pow alpha 2) 1))) (* (PI) (log alpha)))))))))>
#<alt (* 1/2 (/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (* (log alpha) (- 1 (/ 1 (pow alpha 2)))))))))>
#<alt (/ (+ (* 1/2 (/ (- (/ 1 (* (pow alpha 4) (* (PI) (* (log alpha) (pow (- 1 (/ 1 (pow alpha 2))) 2))))) (/ 1 (* (pow alpha 2) (* (PI) (* (log alpha) (pow (- 1 (/ 1 (pow alpha 2))) 2)))))) (pow cosTheta 2))) (* 1/2 (/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (PI) (* (log alpha) (- 1 (/ 1 (pow alpha 2))))))))) (pow cosTheta 2))>
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#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (- (+ (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2))))))>
#<alt (/ (- (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 -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 (pow alpha 2)) 1)>
#<alt (- (* (pow alpha 2) (- (* -1 (pow alpha 2)) 1)) 1)>
#<alt (- (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (pow alpha 2)) 1)) 1)) 1)>
#<alt (/ 1 (pow alpha 2))>
#<alt (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))) (pow alpha 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow alpha 2)) (+ (/ 1 (pow alpha 4)) (/ 1 (pow alpha 6))))) (pow alpha 2))>
#<alt (/ 1 (pow alpha 2))>
#<alt (/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))) (pow alpha 2))>
#<alt (/ (+ 1 (+ (/ 1 (pow alpha 2)) (+ (/ 1 (pow alpha 4)) (/ 1 (pow alpha 6))))) (pow alpha 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<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 (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (log alpha)>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (* -1 (log (/ 1 alpha)))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (+ (log -1) (* -1 (log (/ -1 alpha))))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<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 (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -1 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)>

Calls

78 calls:

Time	Variable		Point	Expression
22.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
5.0ms	cosTheta	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2))))
4.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
2.0ms	cosTheta	@	inf	(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))

rewrite15.0ms (0.2%)

Memory

23.7MiB live, 23.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`
12×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	220

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

22 → 23

Calls

Call 1

Inputs
(/ (- (* alpha alpha) 1) (* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
(- (* alpha alpha) 1)
(* alpha alpha)
(* (* (* alpha alpha) -2) (* (- 0 (* (PI) (log alpha))) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha)))))
(/ (/ 1 (* (PI) (/ 0 0))) (+ -1 (* (* cosTheta cosTheta) 1)))
(/ 1 (* (PI) (/ 0 0)))
(* (PI) (/ 0 0))
(PI)
(/ -1 (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta)))
(* (PI) (log (* alpha alpha)))
(/ (- (* alpha alpha) 1) (* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2))))
(* (* (PI) (log alpha)) (+ 2 (* (* cosTheta cosTheta) -2)))
(/ (/ 1 (/ 1 (+ (* alpha alpha) -1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ 1 (/ 1 (+ (* alpha alpha) -1)))
(/ 1 (+ (* alpha alpha) -1))
(+ (* alpha alpha) -1)
(log alpha)
(* cosTheta cosTheta)
(* (* cosTheta cosTheta) 1)
(log (* alpha alpha))
(* -1 cosTheta)

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

simplify434.0ms (5.1%)

Memory

-15.4MiB live, 643.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 036×	`-lowering-.f32`
7 036×	`-lowering-.f64`
5 604×	`accelerator-lowering-fma.f32`
5 604×	`accelerator-lowering-fma.f64`
3 404×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	481	6698
1	1590	6579
2	6648	6516
0	8414	6268

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

Outputs
(/ -1/2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (log.f32 alpha)))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(-.f32 (.f32 (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.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 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (+.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)) (log.f32 alpha))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(+.f32 (.f32 alpha (.f32 alpha (+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.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 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha (.f32 alpha (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))))) (+.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.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 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (log.f32 alpha))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (.f32 alpha alpha)) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))))
(- (+ (* -1/2 (/ (* (- 1 (pow cosTheta 2)) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (.f32 alpha alpha)) (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
(- (+ (* -1/2 (/ (* (- 1 (pow cosTheta 2)) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (- 1 (pow cosTheta 2)) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(+.f32 (.f32 #s(literal 1/2 binary32) (+.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (.f32 alpha alpha)) (/.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (pow.f32 alpha #s(literal 6 binary32)))))) (+.f32 (.f32 #s(literal -1/2 binary32) (/.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))) (/.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(- (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 4) (* (pow cosTheta 6) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))
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(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (+.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32)))) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.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 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(/.f32 (+.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32)))) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha 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 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
-1
#s(literal -1 binary32)
(- (* -1 (pow alpha 2)) 1)
(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
(- (* (pow alpha 2) (- (* -1 (pow alpha 2)) 1)) 1)
(+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))
(- (* (pow alpha 2) (- (* (pow alpha 2) (- (* -1 (pow alpha 2)) 1)) 1)) 1)
(+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))))))
(/ 1 (pow alpha 2))
(/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2))
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha alpha))
(/ (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))) (pow alpha 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32))) (*.f32 alpha alpha))
(/ (+ 1 (+ (/ 1 (pow alpha 2)) (+ (/ 1 (pow alpha 4)) (/ 1 (pow alpha 6))))) (pow alpha 2))
(/.f32 (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 6 binary32))))) (*.f32 alpha alpha))
(/ 1 (pow alpha 2))
(/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(/ (+ 1 (/ 1 (pow alpha 2))) (pow alpha 2))
(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 alpha alpha))
(/ (+ 1 (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 4)))) (pow alpha 2))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) #s(literal 1 binary32))) (*.f32 alpha alpha))
(/ (+ 1 (+ (/ 1 (pow alpha 2)) (+ (/ 1 (pow alpha 4)) (/ 1 (pow alpha 6))))) (pow alpha 2))
(/.f32 (+.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 6 binary32))))) (*.f32 alpha alpha))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha 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 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(log alpha)
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(pow cosTheta 2)
(*.f32 cosTheta cosTheta)
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* 2 (log alpha))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ 1 alpha)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(* -2 (log (/ -1 alpha)))
(*.f32 (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))
(* -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)

eval36.0ms (0.4%)

Memory: 29.2MiB live, 105.3MiB allocated
Compiler: Compiled 15 637 to 551 computations (96.5% saved)

prune55.0ms (0.6%)

Memory

-18.5MiB live, 137.5MiB allocated

Pruning

34 alts after pruning (28 fresh and 6 done)

	Pruned	Kept	Total
New	515	7	522
Fresh	1	21	22
Picked	3	2	5
Done	0	4	4
Total	519	34	553

Accuracy

100.0%

Counts

553 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.6%	(/.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha))))
✓	77.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
	77.5%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	96.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.3%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.3%	(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 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 alpha)))))) (.f32 (+.f32 (.f32 alpha alpha) (+.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))))
	97.4%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	82.5%	(/.f32 (/.f32 #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))))
	-0.0%	(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
	66.9%	(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (log.f32 alpha)))
	66.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))
	66.3%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	96.2%	(/.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 #s(literal 2 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32)))))
	96.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.8%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.5%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #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 #s(literal -1 binary32) cosTheta) cosTheta))))
	96.6%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	77.7%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.3%	(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 alpha alpha) (PI.f32))) (log.f32 (.f32 alpha alpha)))
	95.9%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))))
	96.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.6%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	66.8%	(/.f32 #s(literal -1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	66.3%	(/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.5%	(+.f32 (+.f32 (/.f32 (/.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.1%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (*.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))))
	97.6%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
	97.4%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 alpha))))
	97.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2 516 to 774 computations (69.2% saved)

regimes80.0ms (0.9%)

Memory

-4.4MiB live, 203.3MiB allocated

Counts

62 → 1

Calls

Call 1

Inputs
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))
(/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (log.f32 alpha)))
(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/.f32 #s(literal -1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal 1 binary32))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))
(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 alpha))))
(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (/.f32 (.f32 alpha alpha) (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 #s(literal 2 binary32) (.f32 (*.f32 cosTheta cosTheta) #s(literal -2 binary32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (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))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha))))
(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (/.f32 #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(literal -1 binary32) (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) (+.f32 #s(literal -1 binary32) (neg.f32 alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #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 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #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 #s(literal -1 binary32) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal 1 binary32)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
(/.f32 (+.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #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 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 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 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.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 alpha alpha)) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (neg.f32 alpha)))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.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 (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.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) (-.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (*.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))))
(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
(/.f32 (/.f32 (neg.f32 (.f32 (pow.f32 alpha #s(literal 5 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 alpha)))))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(+.f32 (+.f32 (/.f32 (/.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(+.f32 (neg.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (.f32 alpha (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal -1 binary32) (log.f32 (.f32 alpha alpha))) (-.f32 (.f32 (pow.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal 4 binary32)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32))))) (.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Outputs

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

Calls

4 calls:

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

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)

regimes52.0ms (0.6%)

Memory

-0.4MiB live, 77.4MiB allocated

Counts

27 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	alpha
8.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.0%	1	`cosTheta`
98.0%	1	`alpha`
98.0%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes60.0ms (0.7%)

Memory

-1.4MiB live, 76.1MiB allocated

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

41.0ms	alpha
8.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.9%	1	`cosTheta`
97.9%	1	`alpha`
97.9%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes25.0ms (0.3%)

Memory

18.9MiB live, 57.3MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	cosTheta
7.0ms	(*.f32 alpha alpha)
7.0ms	alpha

Results

Accuracy	Segments	Branch
97.6%	1	`cosTheta`
97.6%	1	`alpha`
97.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes19.0ms (0.2%)

Memory

24.5MiB live, 62.3MiB allocated

Counts

18 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes11.0ms (0.1%)

Memory

-2.0MiB live, 36.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
66.3%	1	`cosTheta`
66.3%	1	`alpha`
66.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Memory

-19.0MiB live, 23.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(*.f32 alpha alpha)
2.0ms	alpha
2.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify10.0ms (0.1%)

Memory

-14.7MiB live, 23.9MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary32`
18×	`+-commutative_binary32`
8×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	110
1	69	109
2	77	109
3	84	109
4	85	109

Stop Event

1×

saturated

Calls

Call 1

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

soundness811.0ms (9.6%)

Memory

36.1MiB live, 902.2MiB allocated

Rules

9 414×	`accelerator-lowering-fma.f32`
9 414×	`accelerator-lowering-fma.f64`
7 036×	`-lowering-.f32`
7 036×	`-lowering-.f64`
6 606×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	213	2672
1	663	2597
2	2605	2449
0	8225	2336
0	487	6692
1	1592	6388
2	6962	6365
0	8096	6128
0	481	6698
1	1590	6579
2	6648	6516
0	8414	6268
0	13	72
1	88	72
2	758	69
0	8431	61
0	495	9601
1	1649	9359
2	7342	9318
0	8239	8912

Stop Event

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

Compiler

Compiled 303 to 179 computations (40.9% saved)

preprocess80.0ms (0.9%)

Memory

-10.0MiB live, 206.9MiB allocated

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1 002 to 500 computations (50.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze58.0ms (0.7%)

sample1.7s (20.5%)

preprocess483.0ms (5.7%)

explain214.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify383.0ms (4.5%)

localize41.0ms (0.5%)

series62.0ms (0.7%)

rewrite476.0ms (5.6%)

simplify440.0ms (5.2%)

eval95.0ms (1.1%)

prune220.0ms (2.6%)

simplify11.0ms (0.1%)

localize355.0ms (4.2%)

series141.0ms (1.7%)

rewrite16.0ms (0.2%)

simplify707.0ms (8.3%)

eval104.0ms (1.2%)

prune90.0ms (1.1%)

simplify9.0ms (0.1%)

localize247.0ms (2.9%)

series41.0ms (0.5%)

rewrite34.0ms (0.4%)

simplify489.0ms (5.8%)

eval41.0ms (0.5%)

prune41.0ms (0.5%)

simplify10.0ms (0.1%)

localize167.0ms (2%)

series55.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify434.0ms (5.1%)

eval36.0ms (0.4%)

prune55.0ms (0.6%)

regimes80.0ms (0.9%)

regimes52.0ms (0.6%)

regimes60.0ms (0.7%)

regimes25.0ms (0.3%)

regimes19.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

simplify10.0ms (0.1%)

soundness811.0ms (9.6%)

preprocess80.0ms (0.9%)

end0.0ms (0%)

Profiling