Metrics for GTR1 distribution

analyze84.0ms (0.9%)

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 41 to 22 computations (46.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-mult: 16.0ms (29.3% of total)

...c/correct-round.rkt:119:19: 8.0ms (14.7% of total)

ival-<=: 8.0ms (14.7% of total)

ival-sub: 6.0ms (11% of total)

ival-log: 6.0ms (11% of total)

ival-add: 4.0ms (7.3% of total)

ival-div: 3.0ms (5.5% of total)

ival-pi: 2.0ms (3.7% of total)

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

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

sample1.9s (21.2%)

Results

1.6s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-mult: 457.0ms (34.8% of total)

ival-<=: 255.0ms (19.4% of total)

...c/correct-round.rkt:119:19: 187.0ms (14.3% of total)

ival-log: 129.0ms (9.8% of total)

ival-div: 116.0ms (8.8% of total)

ival-sub: 48.0ms (3.7% of total)

ival-add: 44.0ms (3.4% of total)

ival-pi: 34.0ms (2.6% of total)

ival-and: 27.0ms (2.1% of total)

const: 12.0ms (0.9% of total)

backward-pass: 3.0ms (0.2% of total)

Bogosity

preprocess217.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

2506×	`-lowering-.f32`
2506×	`-lowering-.f64`
1886×	`fnmadd-define`
1768×	`fma-lowering-fma.f32`
1768×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	138
1	172	128
2	682	126
3	3796	126
0	13	22
1	43	21
2	158	21
3	680	21
4	2882	21
5	6022	21
0	8031	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 (*.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)))))

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

Symmetry

(abs cosTheta)

(abs alpha)

explain143.0ms (1.6%)

FPErrors

Click to see full error table

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

Results

75.0ms

512×

valid

Compiler

Compiled 214 to 41 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 17.0ms (39.3% of total)

ival-log: 13.0ms (30.1% of total)

ival-div: 4.0ms (9.3% of total)

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

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

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

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 26 to 14 computations (46.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.6%

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

Compiler

Compiled 26 to 13 computations (50% saved)

simplify183.0ms (2%)

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

2506×	`-lowering-.f32`
2506×	`-lowering-.f64`
1886×	`fnmadd-define`
1768×	`fma-lowering-fma.f32`
1768×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	84
1	43	81
2	158	81
3	680	81
4	2882	81
5	6022	81
0	8031	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 (.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) cosTheta)
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)
cosTheta

localize85.0ms (0.9%)

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	99.5%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

69.0ms

256×

valid

Compiler

Compiled 94 to 14 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 12.0ms (55.4% of total)

ival-log: 4.0ms (18.5% of total)

ival-div: 2.0ms (9.2% of total)

ival-pi: 1.0ms (4.6% of total)

ival-sub: 1.0ms (4.6% of total)

ival-add: 1.0ms (4.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series91.0ms (1%)

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
31.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
25.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
14.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
2.0ms	alpha	@	inf	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite396.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

5018×	`-lowering-.f32`
5018×	`-lowering-.f64`
3984×	`/-lowering-/.f32`
3984×	`/-lowering-/.f64`
1616×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	94	64
2	794	61
0	8598	61

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 529

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

simplify333.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

5852×	`-lowering-.f32`
5852×	`-lowering-.f64`
2538×	`/-lowering-/.f32`
2538×	`/-lowering-/.f64`
2264×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	2627
1	710	2409
2	2882	2383
0	8634	2383

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

eval116.0ms (1.3%)

Compiler: Compiled 33065 to 2431 computations (92.6% saved)

prune165.0ms (1.8%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	758	26	784
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	758	27	785

Accuracy

99.8%

Counts

785 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) #s(literal 3 binary32))) (+.f32 (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.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 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.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))))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta (.f32 cosTheta (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) alpha)) (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (-.f32 #s(literal 0 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))))
	94.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	97.7%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha (.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))))
	98.2%	(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) (+.f32 alpha #s(literal 1 binary32))) (+.f32 alpha #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (-.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 alpha alpha)))) (+.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.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))))
	69.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	51.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.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))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 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))))
	98.4%	(/.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))))
	69.2%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.0%	(-.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 cosTheta (.f32 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)))))
	97.4%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))

Compiler

Compiled 1926 to 935 computations (51.5% saved)

simplify12.0ms (0.1%)

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	632

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize322.0ms (3.5%)

Localize:

Found 20 expressions of interest:

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

Results

184.0ms

256×

invalid

Compiler

Compiled 635 to 49 computations (92.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-mult: 35.0ms (45.6% of total)

ival-div: 16.0ms (20.8% of total)

ival-add: 12.0ms (15.6% of total)

ival-sub: 6.0ms (7.8% of total)

ival-log: 4.0ms (5.2% of total)

ival-pi: 1.0ms (1.3% of total)

const: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

backward-pass: 0.0ms (0% of total)

series51.0ms (0.6%)

Counts

26 → 360

Calls

Call 1

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

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

99 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta	@	0	(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms	alpha	@	inf	(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms	cosTheta	@	0	(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	-inf	(* (+ (* alpha (* alpha alpha)) -1) (+ (* alpha (* alpha alpha)) 1))

rewrite20.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	330

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify427.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

6126×	`-lowering-.f32`
6126×	`-lowering-.f64`
4008×	`+-lowering-+.f64`
4008×	`+-lowering-+.f32`
1954×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	647	9733
1	2405	8464
0	9058	8464

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

eval60.0ms (0.7%)

Compiler: Compiled 29980 to 784 computations (97.4% saved)

prune55.0ms (0.6%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	739	15	754
Fresh	8	13	21
Picked	5	0	5
Done	0	1	1
Total	752	29	781

Accuracy

99.9%

Counts

781 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #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 cosTheta cosTheta)))
	94.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.7%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.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))))
▶	85.1%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	69.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	89.5%	(/.f32 (/.f32 #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))))
	97.5%	(/.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)))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	50.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	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 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.2%	(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32)))))))
	96.9%	(/.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	98.3%	(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 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))))
	98.4%	(/.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))))
	69.2%	(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
	97.0%	(-.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 cosTheta (.f32 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)))))
	97.4%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
▶	96.9%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	97.1%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha))))))

Compiler

Compiled 1728 to 937 computations (45.8% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	516

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize240.0ms (2.6%)

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 cosTheta cosTheta)
✓	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 (log.f32 alpha) #s(literal 2 binary32))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(log.f32 alpha)
✓	accuracy	6.3%	(PI.f32)

Results

143.0ms

256×

invalid

Compiler

Compiled 519 to 45 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-mult: 37.0ms (49.2% of total)

ival-div: 15.0ms (19.9% of total)

ival-add: 9.0ms (12% of total)

ival-log: 7.0ms (9.3% of total)

ival-sub: 5.0ms (6.6% of total)

ival-pi: 1.0ms (1.3% of total)

const: 1.0ms (1.3% of total)

backward-pass: 0.0ms (0% of total)

series62.0ms (0.7%)

Counts

25 → 300

Calls

Call 1

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

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

84 calls:

Time	Variable		Point	Expression
12.0ms	alpha	@	-inf	(log alpha)
7.0ms	alpha	@	0	(log alpha)
6.0ms	alpha	@	inf	(log alpha)
3.0ms	alpha	@	0	(/ (+ (* alpha alpha) -1) (* (PI) (log (* alpha alpha))))
2.0ms	alpha	@	0	(/ (/ (- 1 (* alpha alpha)) (* (PI) (/ 0 0))) (+ -1 (* cosTheta cosTheta)))

rewrite27.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	260

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

25 → 25

Calls

Call 1

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

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

simplify380.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

7150×	`-lowering-.f32`
7150×	`-lowering-.f64`
2554×	`+-lowering-+.f64`
2554×	`+-lowering-+.f32`
2270×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	591	7378
1	2178	6487
0	8574	6487

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))))))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 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 (* -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 (* -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 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -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 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha))))
(+ (* -1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1))) (* (PI) (log alpha)))) (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log alpha)))))))
(+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 3))) (* (PI) (log alpha)))) (* 1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))))))))
(* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (+ (* 1/2 (/ (- (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (+ (* 1/2 (/ (- (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (+ (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (+ (* 1/2 (/ (- (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/ (+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))) (+ (* 1/2 (/ (- (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (+ (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 2)))))) (pow cosTheta 2))) (* 1/2 (/ (- (/ 1 (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))) (+ (/ alpha (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))) (/ (* alpha (- alpha 1)) (* (PI) (* (log alpha) (pow (- (pow alpha 2) 1) 4)))))) (pow cosTheta 6)))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* -1 alpha)
(* alpha (- alpha 1))
(* alpha (- alpha 1))
(* alpha (- alpha 1))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 alpha)))
(* (pow alpha 2) (- 1 (/ 1 alpha)))
(* (pow alpha 2) (- 1 (/ 1 alpha)))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 alpha)))
(* (pow alpha 2) (- 1 (/ 1 alpha)))
(* (pow alpha 2) (- 1 (/ 1 alpha)))
-1
(- alpha 1)
(- alpha 1)
(- alpha 1)
alpha
(* alpha (- 1 (/ 1 alpha)))
(* alpha (- 1 (/ 1 alpha)))
(* alpha (- 1 (/ 1 alpha)))
alpha
(* -1 (* alpha (- (/ 1 alpha) 1)))
(* -1 (* alpha (- (/ 1 alpha) 1)))
(* -1 (* alpha (- (/ 1 alpha) 1)))
1
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* -1 (pow alpha 2)))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* -1 (pow alpha 2))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(* (pow alpha 2) (- (/ 1 (pow alpha 2)) 1))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(* -1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log (/ 1 alpha)))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))
(* -1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log (/ -1 alpha)))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ -1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ -1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ -1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ -1 alpha))))))))
(/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))
(- (+ (* (pow cosTheta 2) (- (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ 1 (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ 1 (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(- (+ (* (pow cosTheta 2) (- (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ 1 (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))
(/ (* (pow cosTheta 2) (- (pow alpha 2) 1)) (* (PI) (log (pow alpha 2))))
(* (pow cosTheta 2) (- (+ (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2))))))))
(* (pow cosTheta 2) (- (+ (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2))))))))
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1
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(+ 1 (* -1 (pow alpha 4)))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* -1 (pow alpha 4))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
1
(+ 1 (pow alpha 2))
(+ 1 (pow alpha 2))
(+ 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) (+ 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))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(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 (* -1 (pow cosTheta 2))))))
(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
(- (* 1/2 (* (pow alpha 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
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(- (* (pow alpha 2) (+ (* -1/2 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))) (-.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 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))))
(- (* (pow alpha 2) (+ (* 1/2 (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* (pow alpha 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (+ 1 (* -1 (pow cosTheta 2))))) (* 1/2 (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2)))))) (* -1 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (+ 1 (* -1 (pow cosTheta 2))) 2)))))))) (pow (+ 1 (* -1 (pow cosTheta 2))) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))))
(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))) (-.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) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))) (-.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 #s(literal 1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))
(- (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 alpha alpha)) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (* 1/2 (/ (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (pow alpha 2)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))))
(+.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 alpha alpha)) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
(- (+ (* -1/2 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (* (pow (+ 1 (* -1 (pow cosTheta 2))) 2) (- (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -1 (/ (+ 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 (* -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 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))))) (.f32 alpha alpha)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32))))))) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))))) (+.f32 (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))) (.f32 cosTheta (.f32 cosTheta (pow.f32 alpha #s(literal 4 binary32))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(- (* 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 #s(literal 1/2 binary32) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.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 (* -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 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 alpha #s(literal 4 binary32))))) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.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 (* -1 (pow cosTheta 2))) 2) (* (pow alpha 6) (* (pow cosTheta 8) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* 1/2 (/ (+ 1 (* -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 #s(literal 1/2 binary32) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 alpha #s(literal 4 binary32)))))) (+.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)))) (.f32 (.f32 (PI.f32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (pow.f32 cosTheta #s(literal 8 binary32)) (pow.f32 alpha #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 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha))))
(/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
(+ (* -1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1))) (* (PI) (log alpha)))) (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (.f32 #s(literal -1/2 binary32) (.f32 (+.f32 (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha) #s(literal -1 binary32)) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (.f32 (PI.f32) (log.f32 alpha))))
(+ (* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2))) (* (PI) (log alpha)))))))
(+.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (+.f32 (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha) #s(literal -1 binary32)) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 alpha))) #s(literal -1/2 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) #s(literal -1/2 binary32)) (/.f32 (.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 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (- (pow alpha 2) 1)) (* (PI) (log alpha)))) (* (pow cosTheta 2) (+ (* -1/2 (/ (* (pow cosTheta 2) (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 3))) (* (PI) (log alpha)))) (* 1/2 (/ (* (- (+ alpha (* alpha (- alpha 1))) 1) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))))))))
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(* 1/2 (/ (- (+ alpha (* alpha (- alpha 1))) 1) (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
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(/ (+ (* -1 (/ (- 1 (pow alpha 2)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (pow cosTheta 2))))) (pow cosTheta 2))
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(* -1 (/ (- 1 (pow alpha 2)) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))))
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(/ (+ (* -1 (/ (- 1 (pow alpha 2)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (* -1 (/ (- (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (pow cosTheta 2)))) (pow cosTheta 2))
(/.f32 (neg.f32 (+.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (/.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (.f32 cosTheta cosTheta)))) (.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- 1 (pow alpha 2)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (* -1 (/ (- (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (pow cosTheta 2))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (/.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (*.f32 cosTheta cosTheta))
(/ (+ (* -1 (/ (- 1 (pow alpha 2)) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1))))) (+ (* -1 (/ (- (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3)))) (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 3))))) (pow cosTheta 4))) (+ (* -1 (/ (- (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2)))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 2))))) (pow cosTheta 2))) (* -1 (/ (- (/ (pow alpha 2) (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4)))) (/ 1 (* (PI) (* (log (pow alpha 2)) (pow (- (pow alpha 2) 1) 4))))) (pow cosTheta 6)))))) (pow cosTheta 2))
(/.f32 (-.f32 (-.f32 (-.f32 (/.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 4 binary32)) (PI.f32)))) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) #s(literal 4 binary32)) (log.f32 (.f32 alpha alpha))))) (pow.f32 cosTheta #s(literal 6 binary32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (*.f32 cosTheta cosTheta))
-1
#s(literal -1 binary32)
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(- (pow alpha 2) 1)
(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
1
#s(literal 1 binary32)
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(+ 1 (* -1 (pow alpha 4)))
(-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* -1 (pow alpha 4))
(-.f32 #s(literal 0 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* -1 (pow alpha 4))
(-.f32 #s(literal 0 binary32) (pow.f32 alpha #s(literal 4 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
(* (pow alpha 4) (- (/ 1 (pow alpha 4)) 1))
(*.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32))) #s(literal -1 binary32)))
1
#s(literal 1 binary32)
(+ 1 (pow alpha 2))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(+ 1 (pow alpha 2))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(+ 1 (pow alpha 2))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(pow alpha 2)
(*.f32 alpha alpha)
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))
(* (pow alpha 2) (+ 1 (/ 1 (pow alpha 2))))
(+.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)))
(* 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) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* 2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 #s(literal 2 binary32) (-.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 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* 2 (* (PI) (log alpha)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (PI.f32) (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (PI.f32) #s(literal -2 binary32)))

eval45.0ms (0.5%)

Compiler: Compiled 20326 to 675 computations (96.7% saved)

prune50.0ms (0.5%)

Pruning

33 alts after pruning (29 fresh and 4 done)

	Pruned	Kept	Total
New	563	13	576
Fresh	7	16	23
Picked	2	3	5
Done	0	1	1
Total	572	33	605

Accuracy

99.9%

Counts

605 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
▶	94.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.7%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.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))))
▶	-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)))
	69.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	89.5%	(/.f32 (/.f32 #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))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	50.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	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 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.8%	(/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) #s(literal -1/2 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))
	68.7%	(/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))
▶	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.2%	(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32)))))))
	96.9%	(/.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.3%	(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 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 alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.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))))
	69.2%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	82.4%	(/.f32 #s(literal -1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))
	97.0%	(-.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 cosTheta (.f32 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)))))
	97.4%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	68.8%	(.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
✓	96.9%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.6%	(.f32 (/.f32 (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.6%	(.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.5%	(.f32 (.f32 (.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	51.0%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))

Compiler

Compiled 1770 to 984 computations (44.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32)))
✓	cost-diff	(-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))
✓	cost-diff	(/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))
✓	cost-diff	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	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 alpha alpha)
✓	cost-diff	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	cost-diff	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	cost-diff	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	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 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 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.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-/.f32`
20×	`/-lowering-/.f64`
12×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	513

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

localize293.0ms (3.2%)

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

Results

153.0ms

256×

invalid

Compiler

Compiled 516 to 45 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 77.0ms

ival-mult: 39.0ms (50.7% of total)

ival-div: 16.0ms (20.8% of total)

ival-log: 7.0ms (9.1% of total)

ival-add: 7.0ms (9.1% of total)

ival-sub: 4.0ms (5.2% of total)

ival-pi: 3.0ms (3.9% of total)

const: 1.0ms (1.3% of total)

backward-pass: 0.0ms (0% of total)

series54.0ms (0.6%)

Counts

26 → 300

Calls

Call 1

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

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

78 calls:

Time	Variable		Point	Expression
25.0ms	cosTheta	@	inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
4.0ms	cosTheta	@	inf	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
3.0ms	alpha	@	inf	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	-inf	(/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	282

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify379.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

7688×	`-lowering-.f32`
7688×	`-lowering-.f64`
3476×	`+-lowering-+.f64`
3476×	`+-lowering-+.f32`
1924×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	8457
1	2292	7644
0	8880	7644

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

eval57.0ms (0.6%)

Compiler: Compiled 22725 to 697 computations (96.9% saved)

prune54.0ms (0.6%)

Pruning

36 alts after pruning (29 fresh and 7 done)

	Pruned	Kept	Total
New	526	12	538
Fresh	7	17	24
Picked	2	3	5
Done	0	4	4
Total	535	36	571

Accuracy

100.0%

Counts

571 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	89.8%	(/.f32 (/.f32 (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	94.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.7%	(/.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 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.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))))
	-0.0%	(/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) #s(literal -1 binary32))
	69.3%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	89.5%	(/.f32 (/.f32 #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))))
	67.7%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	94.3%	(/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	50.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.5%	(/.f32 (+.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1 binary32) (PI.f32))) (log.f32 (.f32 alpha alpha)))
✓	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 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	68.7%	(/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))
✓	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.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))))
	94.2%	(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha (+.f32 alpha #s(literal -1 binary32)))))))
	96.9%	(/.f32 (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.3%	(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 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 alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.3%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
	94.6%	(/.f32 (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (*.f32 (PI.f32) (log.f32 alpha)))
	69.2%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	67.7%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	82.4%	(/.f32 #s(literal -1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))
	97.0%	(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	97.4%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (PI.f32)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	68.8%	(.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
✓	96.9%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.6%	(.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	51.0%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
	94.4%	(.f32 (.f32 alpha alpha) (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha (.f32 alpha (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2836 to 826 computations (70.9% saved)

regimes86.0ms (0.9%)

Counts

67 → 1

Calls

Call 1

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

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:

25.0ms	(*.f32 alpha alpha)
19.0ms	cosTheta
19.0ms	alpha
18.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes29.0ms (0.3%)

Counts

28 → 1

Calls

Call 1

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

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)
9.0ms	cosTheta
8.0ms	alpha

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes24.0ms (0.3%)

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

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes24.0ms (0.3%)

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

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

Calls

3 calls:

9.0ms	alpha
7.0ms	(*.f32 alpha alpha)
7.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.9%	1	`cosTheta`
96.9%	1	`alpha`
96.9%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes21.0ms (0.2%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes20.0ms (0.2%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes14.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
69.2%	1	`cosTheta`
69.2%	1	`alpha`
69.2%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
68.8%	1	`alpha`
68.8%	1	`(*.f32 alpha alpha)`
68.8%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes15.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

Calls

3 calls:

9.0ms	alpha
3.0ms	(*.f32 alpha alpha)
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
67.7%	1	`cosTheta`
67.7%	1	`alpha`
67.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

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)))) #s(literal -1 binary32))
(/.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 (-.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 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 cosTheta (.f32 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:

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

Results

Accuracy	Segments	Branch
67.7%	1	`alpha`
67.7%	1	`(*.f32 alpha alpha)`
67.7%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

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)))) #s(literal -1 binary32))
(/.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 (-.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 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 cosTheta (.f32 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)))) #s(literal -1 binary32))

Calls

3 calls:

3.0ms	alpha
2.0ms	cosTheta
2.0ms	(*.f32 alpha 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%)

Algorithm

1×	egg-herbie

Rules

34×	`*-commutative_binary32`
14×	`+-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	48	155
1	74	155
2	83	155
3	91	155
4	93	155

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.4s (26.1%)

Rules

7688×	`-lowering-.f32`
7688×	`-lowering-.f64`
7150×	`-lowering-.f32`
7150×	`-lowering-.f64`
6126×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	647	9733
1	2405	8464
0	9058	8464
0	213	2627
1	710	2409
2	2882	2383
0	8634	2383
0	13	66
1	94	64
2	794	61
0	8598	61
0	624	8457
1	2292	7644
0	8880	7644
0	591	7378
1	2178	6487
0	8574	6487

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 502 to 281 computations (44% saved)

preprocess78.0ms (0.8%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1198 to 564 computations (52.9% saved)

analyze84.0ms (0.9%)

sample1.9s (21.2%)

preprocess217.0ms (2.4%)

explain143.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify183.0ms (2%)

localize85.0ms (0.9%)

series91.0ms (1%)

rewrite396.0ms (4.3%)

simplify333.0ms (3.6%)

eval116.0ms (1.3%)

prune165.0ms (1.8%)

simplify12.0ms (0.1%)

localize322.0ms (3.5%)

series51.0ms (0.6%)

rewrite20.0ms (0.2%)

simplify427.0ms (4.7%)

eval60.0ms (0.7%)

prune55.0ms (0.6%)

simplify12.0ms (0.1%)

localize240.0ms (2.6%)

series62.0ms (0.7%)

rewrite27.0ms (0.3%)

simplify380.0ms (4.1%)

eval45.0ms (0.5%)

prune50.0ms (0.5%)

simplify10.0ms (0.1%)

localize293.0ms (3.2%)

series54.0ms (0.6%)

rewrite62.0ms (0.7%)

simplify379.0ms (4.1%)

eval57.0ms (0.6%)

prune54.0ms (0.6%)

regimes86.0ms (0.9%)

regimes29.0ms (0.3%)

regimes24.0ms (0.3%)

regimes24.0ms (0.3%)

regimes21.0ms (0.2%)

regimes20.0ms (0.2%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes15.0ms (0.2%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

simplify10.0ms (0.1%)

soundness2.4s (26.1%)

preprocess78.0ms (0.8%)

end0.0ms (0%)

Profiling