Metrics for GTR1 distribution

analyze55.0ms (0.7%)

Memory

9.0MiB live, 125.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 40 to 23 computations (42.5% saved)

sample1.6s (18.7%)

Memory

-84.5MiB live, 1 935.1MiB allocated

Samples

1.3s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 811.0ms

ival-mult: 259.0ms (32% of total)

ival-log: 125.0ms (15.4% of total)

const: 116.0ms (14.3% of total)

ival-<=: 81.0ms (10% of total)

ival-div: 71.0ms (8.8% of total)

ival-sub: 46.0ms (5.7% of total)

ival-add: 45.0ms (5.6% of total)

ival-pi: 30.0ms (3.7% of total)

ival-and: 23.0ms (2.8% of total)

exact: 10.0ms (1.2% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

preprocess458.0ms (5.4%)

Memory

20.2MiB live, 635.1MiB 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)

explain172.0ms (2%)

Memory

-20.3MiB live, 293.1MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

62.0ms

512×

valid

Compiler

Compiled 238 to 56 computations (76.5% saved)

Precisions

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

ival-mult: 26.0ms (59.1% of total)

ival-log: 7.0ms (15.9% of total)

ival-div: 4.0ms (9.1% of total)

ival-pi: 2.0ms (4.5% of total)

ival-add: 2.0ms (4.5% of total)

ival-sub: 2.0ms (4.5% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.5%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify425.0ms (5%)

Memory

24.5MiB live, 616.2MiB 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

localize44.0ms (0.5%)

Memory

-26.7MiB live, 70.2MiB 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

28.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 10.0ms (49.5% of total)

ival-div: 4.0ms (19.8% of total)

ival-log: 3.0ms (14.8% of total)

ival-pi: 1.0ms (4.9% of total)

ival-add: 1.0ms (4.9% of total)

ival-sub: 1.0ms (4.9% 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

20.0MiB live, 134.3MiB 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
19.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
12.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
10.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
2.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite691.0ms (8.2%)

Memory

-7.4MiB live, 617.2MiB 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)))

simplify583.0ms (6.9%)

Memory

-10.5MiB live, 615.2MiB 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)))

eval178.0ms (2.1%)

Memory: 9.2MiB live, 198.9MiB allocated
Compiler: Compiled 40 972 to 3 131 computations (92.4% saved)

prune289.0ms (3.4%)

Memory

20.3MiB live, 340.7MiB allocated

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	1 011	25	1 036
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1 012	25	1 037

Accuracy

99.9%

Counts

1 037 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(/.f32 (fma.f32 (+.f32 alpha #s(literal -1 binary32)) alpha (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (/.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)))))
	98.4%	(/.f32 (/.f32 (+.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	97.8%	(/.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))))
	97.8%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #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))))
	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))))
	98.1%	(/.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))))
	65.2%	(/.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))))))
	97.8%	(/.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))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	97.9%	(/.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))))
	54.0%	(/.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))))))
	95.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))
	98.5%	(/.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 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))))
	98.3%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.4%	(/.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))))
	1.9%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	98.1%	(+.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 #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 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 1 610 to 850 computations (47.2% saved)

simplify25.0ms (0.3%)

Memory

-32.3MiB live, 19.7MiB 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 #s(literal 1 binary32) alpha)) (+.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 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	(+.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))))
✓	cost-diff	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 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 (neg.f32 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)) (.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 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 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 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
18×	`+-lowering-+.f64`
18×	`/-lowering-/.f32`
18×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	533

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

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

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

localize189.0ms (2.2%)

Memory

6.3MiB live, 360.0MiB 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 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 (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 cosTheta cosTheta)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

82.0ms

256×

invalid

Compiler

Compiled 552 to 47 computations (91.5% saved)

Precisions

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

ival-mult: 26.0ms (43.1% of total)

ival-div: 13.0ms (21.6% of total)

ival-add: 12.0ms (19.9% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series67.0ms (0.8%)

Memory

-10.8MiB live, 64.9MiB allocated

Counts

23 → 300

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 (/ (/ (- 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) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))>
#<alt (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))>
#<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 (+ 1 (/ -1 (* alpha alpha)))>
#<alt (/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))>
#<alt (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1)))>
#<alt (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1))>
#<alt (+ (* alpha (* alpha alpha)) 1)>
#<alt (PI)>
#<alt (log (* alpha alpha))>
#<alt (* cosTheta cosTheta)>
#<alt (* (PI) (/ 0 0))>
#<alt (neg cosTheta)>
#<alt (* (PI) (log (* alpha 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 (/ (- (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 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) (+ 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)))))))))>
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#<alt (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 4))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))) (* -1 (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 3)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha)))))))) (/ (* (+ 1 (pow alpha 3)) (pow (- (pow alpha 2) 1) 2)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (/ (* (+ 1 (pow alpha 3)) (- (pow alpha 2) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))>
#<alt (/ (+ 1 (pow alpha 3)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))>
#<alt (/ (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 6))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (- (+ 1 (pow alpha 2)) alpha))))))) (+ (* -1 (/ (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (* (pow cosTheta 4) (- (pow alpha 2) 1)))) (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 alpha) (* (- (+ 1 (pow alpha 2)) alpha) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt -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 (pow alpha 5)>
#<alt (* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 3))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 5)))))>
#<alt (pow alpha 5)>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))>
#<alt (* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) (+ 1 (/ 1 (pow alpha 3))))))>
#<alt (* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- 1 (/ 1 (pow alpha 2))) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))>
#<alt 1>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<alt (+ 1 (pow alpha 3))>
#<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 (* (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 (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* 2 (log alpha))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ 1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (* -2 (log (/ -1 alpha)))>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* 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 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

84 calls:

Time	Variable		Point	Expression
3.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta)))
3.0ms	cosTheta	@	0	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/ (/ (* (+ (* alpha (* alpha alpha)) 1) (+ (* alpha alpha) -1)) (* (+ (* alpha alpha) (- 1 alpha)) (+ alpha 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite15.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
18×	`+-lowering-+.f64`
18×	`/-lowering-/.f32`
18×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	273

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 24

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

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

simplify445.0ms (5.3%)

Memory

11.0MiB live, 637.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6 484×	`-lowering-.f32`
6 484×	`-lowering-.f64`
5 106×	`accelerator-lowering-fma.f32`
5 106×	`accelerator-lowering-fma.f64`
3 934×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	496	8718
1	1642	8239
2	7625	8203
0	8007	7892

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

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

eval54.0ms (0.6%)

Memory: 0.5MiB live, 113.6MiB allocated
Compiler: Compiled 24 063 to 653 computations (97.3% saved)

prune63.0ms (0.7%)

Memory

6.1MiB live, 99.2MiB allocated

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	652	14	666
Fresh	5	15	20
Picked	4	1	5
Done	0	0	0
Total	661	30	691

Accuracy

100.0%

Counts

691 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	-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))))
	98.4%	(/.f32 (/.f32 (+.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	84.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha))) (.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))))
▶	76.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.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))))
	95.5%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #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))))
	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))))
	98.1%	(/.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))))
	65.2%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	65.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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))))))
	97.8%	(/.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))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	54.0%	(/.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))))))
	95.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 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 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))))
▶	98.3%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.2%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha alpha) alpha))))))
	97.8%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.4%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	1.9%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	65.2%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.1%	(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
▶	95.5%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	97.4%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (.f32 (PI.f32) (.f32 alpha 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)))))))

Compiler

Compiled 1 668 to 957 computations (42.6% saved)

simplify12.0ms (0.1%)

Memory

-17.3MiB live, 20.8MiB 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 #s(literal 1 binary32) alpha)) (+.f32 alpha #s(literal 1 binary32))))
✓	cost-diff	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.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))))
✓	cost-diff	(+.f32 alpha #s(literal -1 binary32))
✓	cost-diff	(+.f32 alpha #s(literal 1 binary32))
✓	cost-diff	(*.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32)))
✓	cost-diff	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	(/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))) (PI.f32))
✓	cost-diff	(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	cost-diff	(*.f32 alpha alpha)
✓	cost-diff	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.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 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (*.f32 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 #s(literal 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	500

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

localize229.0ms (2.7%)

Memory

38.2MiB live, 307.9MiB allocated

Localize:

Found 20 expressions of interest:

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

Samples

130.0ms

256×

invalid

Compiler

Compiled 506 to 49 computations (90.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-div: 38.0ms (43.9% of total)

ival-mult: 25.0ms (28.8% of total)

ival-add: 11.0ms (12.7% of total)

ival-log: 6.0ms (6.9% of total)

ival-sub: 4.0ms (4.6% of total)

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

exact: 1.0ms (1.2% of total)

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

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

series71.0ms (0.8%)

Memory

9.8MiB live, 162.0MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

78 calls:

Time	Variable		Point	Expression
8.0ms	alpha	@	-inf	(log alpha)
8.0ms	alpha	@	inf	(log alpha)
6.0ms	alpha	@	-inf	(* 2 (* (* (PI) (log alpha)) (+ (- 1 (* cosTheta cosTheta)) (* alpha (* alpha (* cosTheta cosTheta))))))
6.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* 2 (* (* (PI) (log alpha)) (+ (- 1 (* cosTheta cosTheta)) (* alpha (* alpha (* cosTheta cosTheta)))))))
4.0ms	alpha	@	0	(log alpha)

rewrite17.0ms (0.2%)

Memory

-3.0MiB live, 33.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	246

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 23

Calls

Call 1

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

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

simplify437.0ms (5.2%)

Memory

-24.9MiB live, 782.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 324×	`-lowering-.f32`
7 324×	`-lowering-.f64`
5 864×	`accelerator-lowering-fma.f32`
5 864×	`accelerator-lowering-fma.f64`
4 046×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	569	6665
1	1944	6300
0	8436	6043

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

Outputs
(/ -1/2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(- (* 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) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.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 #s(literal -1/2 binary32) (.f32 (PI.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 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.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 #s(literal -1/2 binary32) (.f32 alpha alpha))) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.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 #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 (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 (.f32 alpha alpha) (+.f32 (.f32 (.f32 alpha alpha) (+.f32 (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.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 #s(literal 1/2 binary32) (/.f32 (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.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 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 alpha 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 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.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 #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 (/.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 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)))))))
(-.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (.f32 alpha alpha)) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (*.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 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (.f32 alpha alpha)) (-.f32 (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (*.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))))) (+.f32 (/.f32 (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (.f32 alpha alpha)) (-.f32 (/.f32 (.f32 (.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 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)) (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.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 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))))
(- (+ (* 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)))))))))
(+.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32)))))))
(- (+ (* -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)))))))))
(+.f32 (/.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (pow.f32 alpha #s(literal 6 binary32))) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 8 binary32))))) (+.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 6 binary32))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (pow.f32 cosTheta #s(literal 4 binary32))))))))
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (PI) (log alpha)))))))
(+.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (*.f32 (PI.f32) (log.f32 alpha))))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (pow (- (pow alpha 2) 1) 2) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (PI) (log alpha)))) (* 1/2 (/ (pow (- (pow alpha 2) 1) 3) (* (PI) (log alpha)))))))))
(+.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (pow.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 4 binary32))) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 alpha))))))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (log alpha))))
(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta))
(/ (- (* 1/2 (/ 1 (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))) (pow cosTheta 2))
(/.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (*.f32 cosTheta cosTheta))
(/ (- (+ (/ 1/2 (* (pow cosTheta 4) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2))))) (* 1/2 (/ 1 (* (PI) (log alpha))))) (/ 1/2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
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(/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) #s(literal 1 binary32)) alpha)
(* -1 (/ (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1) alpha))
(/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32))) (neg.f32 alpha))
(* -1 (/ (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1) alpha))
(/.f32 (+.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32)) alpha) (.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) #s(literal -1 binary32))) (neg.f32 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)
(* 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 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* 2 (* (PI) (log alpha)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (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)))

eval40.0ms (0.5%)

Memory: 3.5MiB live, 119.0MiB allocated
Compiler: Compiled 17 473 to 630 computations (96.4% saved)

prune47.0ms (0.6%)

Memory

13.3MiB live, 175.2MiB allocated

Pruning

35 alts after pruning (31 fresh and 4 done)

	Pruned	Kept	Total
New	526	11	537
Fresh	4	20	24
Picked	2	3	5
Done	0	1	1
Total	532	35	567

Accuracy

100.0%

Counts

567 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	74.4%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 alpha alpha) alpha))))
▶	98.4%	(/.f32 (/.f32 (+.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #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))))
	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))))
	98.1%	(/.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))))
	65.2%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	65.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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))))))
	97.8%	(/.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))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	54.0%	(/.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))))))
	95.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
▶	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 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))))
✓	98.3%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (+.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))))
	95.2%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha alpha) alpha))))))
	97.8%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.4%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	64.2%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
▶	65.2%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.1%	(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	95.5%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
✓	95.5%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	64.2%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
▶	95.3%	(.f32 (.f32 alpha alpha) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha))))
	95.4%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1 696 to 997 computations (41.2% saved)

simplify11.0ms (0.1%)

Memory

-13.9MiB live, 25.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

32×	`-lowering-.f32`
32×	`-lowering-.f64`
20×	`+-lowering-+.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	485

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize180.0ms (2.1%)

Memory

9.3MiB live, 451.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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 (PI.f32) (.f32 alpha alpha))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(neg.f32 cosTheta)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)
✓	accuracy	100.0%	(.f32 (.f32 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 alpha (.f32 alpha alpha))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	6.3%	(PI.f32)

Samples

105.0ms

256×

invalid

Compiler

Compiled 499 to 48 computations (90.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 31.0ms (47.2% of total)

ival-div: 14.0ms (21.3% of total)

ival-add: 11.0ms (16.7% of total)

ival-log: 4.0ms (6.1% of total)

ival-neg: 2.0ms (3% of total)

ival-pi: 1.0ms (1.5% of total)

ival-sub: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series51.0ms (0.6%)

Memory

-11.7MiB live, 143.3MiB allocated

Counts

26 → 312

Calls

Call 1

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

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

Calls

81 calls:

Time	Variable		Point	Expression
22.0ms	alpha	@	inf	(/ (/ (+ (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))) -1) (+ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (/ (+ (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))) -1) (+ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	inf	(/ (+ (* alpha (+ alpha 1)) (+ -1 (neg alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (+ (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))) -1) (+ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (/ (+ (* (* alpha alpha) (* alpha (* alpha (* alpha alpha)))) -1) (+ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite20.0ms (0.2%)

Memory

10.4MiB live, 44.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

32×	`-lowering-.f32`
32×	`-lowering-.f64`
20×	`+-lowering-+.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	273

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 28

Calls

Call 1

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

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

simplify404.0ms (4.8%)

Memory

29.5MiB live, 826.3MiB allocated

Algorithm

1×	egg-herbie

Rules

5 268×	`-lowering-.f32`
5 268×	`-lowering-.f64`
4 952×	`accelerator-lowering-fma.f32`
4 952×	`accelerator-lowering-fma.f64`
3 622×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	482	7136
1	1590	6688
2	7365	6601
0	8020	6354

Stop Event

1×	iter limit
1×	node limit

Counts

312 → 312

Calls

Call 1

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

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

eval88.0ms (1%)

Memory: -37.2MiB live, 98.7MiB allocated
Compiler: Compiled 19 792 to 531 computations (97.3% saved)

prune53.0ms (0.6%)

Memory

3.2MiB live, 162.8MiB allocated

Pruning

41 alts after pruning (34 fresh and 7 done)

	Pruned	Kept	Total
New	556	10	566
Fresh	2	24	26
Picked	2	3	5
Done	0	4	4
Total	560	41	601

Accuracy

100.0%

Counts

601 → 41

Alt Table

Click to see full alt table

Status	Accuracy	Program
	74.4%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 alpha alpha) alpha))))
	95.2%	(/.f32 (/.f32 (+.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	98.4%	(/.f32 (/.f32 (+.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 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.4%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 6 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (*.f32 alpha alpha) (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32))))) (PI.f32))
	97.8%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #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))))
	98.1%	(/.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 cosTheta cosTheta)))
	65.2%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	65.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	64.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))
	87.3%	(/.f32 (/.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))))
	64.3%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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))))))
	97.8%	(/.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))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	54.0%	(/.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))))))
	95.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
✓	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))))
✓	98.3%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.6%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (+.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))))
	95.2%	(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (*.f32 alpha alpha) alpha))))))
	97.8%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.4%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	64.2%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	65.2%	(/.f32 #s(literal -1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	64.2%	(/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.1%	(.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	95.2%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) alpha) alpha) (log.f32 (.f32 alpha alpha))))
	95.5%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
✓	95.5%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	64.2%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 alpha))))
	64.2%	(.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
✓	95.3%	(.f32 (.f32 alpha alpha) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha)))) (log.f32 (*.f32 alpha alpha))))
	95.4%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2 442 to 838 computations (65.7% saved)

regimes75.0ms (0.9%)

Memory

-4.6MiB live, 191.6MiB allocated

Counts

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes41.0ms (0.5%)

Memory

22.6MiB live, 98.8MiB allocated

Counts

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

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:

11.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
10.0ms	alpha
9.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes31.0ms (0.4%)

Memory

-0.1MiB live, 80.5MiB allocated

Counts

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

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

Calls

3 calls:

10.0ms	(*.f32 alpha alpha)
10.0ms	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

-17.1MiB live, 61.2MiB allocated

Counts

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

Outputs
(/.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))))

Calls

3 calls:

8.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta
7.0ms	alpha

Results

Accuracy	Segments	Branch
97.8%	1	`cosTheta`
97.8%	1	`alpha`
97.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes28.0ms (0.3%)

Memory

7.7MiB live, 53.9MiB allocated

Counts

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

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

Calls

3 calls:

13.0ms	alpha
7.0ms	(*.f32 alpha alpha)
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.1%	1	`cosTheta`
97.1%	1	`alpha`
97.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes68.0ms (0.8%)

Memory

-19.8MiB live, 58.0MiB 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 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 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 #s(literal 2 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 #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 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 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 (neg.f32 cosTheta) cosTheta))))
(.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 (-.f32 (.f32 alpha (+.f32 alpha #s(literal 1 binary32))) alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(.f32 (.f32 alpha alpha) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))

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

Calls

3 calls:

30.0ms	cosTheta
7.0ms	(*.f32 alpha alpha)
6.0ms	alpha

Results

Accuracy	Segments	Branch
95.6%	1	`alpha`
95.6%	1	`(*.f32 alpha alpha)`
95.6%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes13.0ms (0.2%)

Memory

36.5MiB live, 36.6MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.5%	1	`cosTheta`
95.5%	1	`alpha`
95.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes11.0ms (0.1%)

Memory

-2.0MiB live, 36.7MiB allocated

Counts

9 → 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 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 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
64.3%	1	`cosTheta`
64.3%	1	`alpha`
64.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Memory

-16.8MiB live, 23.2MiB allocated

Counts

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

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

Calls

3 calls:

4.0ms	cosTheta
2.0ms	alpha
2.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
64.2%	1	`alpha`
64.2%	1	`(*.f32 alpha alpha)`
64.2%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

Memory

-17.8MiB live, 21.3MiB 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:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify10.0ms (0.1%)

Memory

34.2MiB live, 34.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	151
1	75	151
2	84	151
3	93	151
4	95	151

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

soundness1.0s (12.2%)

Memory

15.3MiB live, 1 277.8MiB allocated

Rules

9 414×	`accelerator-lowering-fma.f32`
9 414×	`accelerator-lowering-fma.f64`
7 324×	`-lowering-.f32`
7 324×	`-lowering-.f64`
6 606×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	496	8718
1	1642	8239
2	7625	8203
0	8007	7892
0	213	2672
1	663	2597
2	2605	2449
0	8225	2336
0	482	7136
1	1590	6688
2	7365	6601
0	8020	6354
0	13	72
1	88	72
2	758	69
0	8431	61
0	569	6665
1	1944	6300
0	8436	6043

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 490 to 262 computations (46.5% saved)

preprocess55.0ms (0.6%)

Memory

6.9MiB live, 204.8MiB allocated

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1 190 to 562 computations (52.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze55.0ms (0.7%)

sample1.6s (18.7%)

preprocess458.0ms (5.4%)

explain172.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify425.0ms (5%)

localize44.0ms (0.5%)

series62.0ms (0.7%)

rewrite691.0ms (8.2%)

simplify583.0ms (6.9%)

eval178.0ms (2.1%)

prune289.0ms (3.4%)

simplify25.0ms (0.3%)

localize189.0ms (2.2%)

series67.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify445.0ms (5.3%)

eval54.0ms (0.6%)

prune63.0ms (0.7%)

simplify12.0ms (0.1%)

localize229.0ms (2.7%)

series71.0ms (0.8%)

rewrite17.0ms (0.2%)

simplify437.0ms (5.2%)

eval40.0ms (0.5%)

prune47.0ms (0.6%)

simplify11.0ms (0.1%)

localize180.0ms (2.1%)

series51.0ms (0.6%)

rewrite20.0ms (0.2%)

simplify404.0ms (4.8%)

eval88.0ms (1%)

prune53.0ms (0.6%)

regimes75.0ms (0.9%)

regimes41.0ms (0.5%)

regimes31.0ms (0.4%)

regimes25.0ms (0.3%)

regimes28.0ms (0.3%)

regimes68.0ms (0.8%)

regimes13.0ms (0.2%)

regimes11.0ms (0.1%)

regimes10.0ms (0.1%)

regimes7.0ms (0.1%)

simplify10.0ms (0.1%)

soundness1.0s (12.2%)

preprocess55.0ms (0.6%)

end0.0ms (0%)

Profiling