Metrics for GTR1 distribution

analyze90.0ms (1%)

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: 50.0ms

ival-mult: 15.0ms (30% of total)

...c/correct-round.rkt:119:19: 9.0ms (18% of total)

ival-<=: 8.0ms (16% of total)

ival-log: 6.0ms (12% of total)

ival-div: 3.0ms (6% of total)

ival-add: 3.0ms (6% of total)

ival-sub: 3.0ms (6% of total)

ival-pi: 2.0ms (4% of total)

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

const: 1.0ms (2% of total)

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

sample1.7s (18.7%)

Results

1.4s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-mult: 348.0ms (31.9% of total)

...c/correct-round.rkt:119:19: 175.0ms (16% of total)

ival-<=: 173.0ms (15.8% of total)

ival-log: 155.0ms (14.2% of total)

ival-div: 69.0ms (6.3% of total)

ival-add: 48.0ms (4.4% of total)

ival-sub: 47.0ms (4.3% of total)

ival-pi: 37.0ms (3.4% of total)

ival-and: 26.0ms (2.4% of total)

const: 11.0ms (1% of total)

backward-pass: 3.0ms (0.3% of total)

Bogosity

preprocess224.0ms (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	128
1	175	116
2	686	114
3	3787	114
0	13	21
1	44	19
2	160	19
3	684	19
4	2882	19
5	6032	19
0	8041	19

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

Symmetry

(abs cosTheta)

(abs alpha)

explain441.0ms (4.8%)

FPErrors

Click to see full error table

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

Results

115.0ms

512×

valid

Compiler

Compiled 214 to 41 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 19.0ms (47.7% of total)

ival-log: 9.0ms (22.6% of total)

ival-div: 4.0ms (10% of total)

ival-sub: 3.0ms (7.5% of total)

ival-add: 3.0ms (7.5% of total)

ival-pi: 2.0ms (5% of total)

const: 1.0ms (2.5% 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
▶	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.4%	(/.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

▶

98.3%

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

▶

98.4%

(/.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 52 to 27 computations (48.1% saved)

simplify174.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

2558×	`-lowering-.f32`
2558×	`-lowering-.f64`
1740×	`+-lowering-+.f64`
1740×	`+-lowering-+.f32`
1464×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	146
1	71	140
2	230	140
3	1079	140
4	3713	139
5	7052	139
0	8057	139

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

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

localize204.0ms (2.2%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.5%	(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
✓	accuracy	98.8%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	99.7%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.2%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	98.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

175.0ms

256×

valid

Compiler

Compiled 181 to 22 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-div: 127.0ms (83.1% of total)

ival-mult: 13.0ms (8.5% of total)

ival-add: 6.0ms (3.9% of total)

ival-log: 4.0ms (2.6% of total)

ival-pi: 1.0ms (0.7% of total)

ival-sub: 1.0ms (0.7% of total)

const: 1.0ms (0.7% of total)

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

series82.0ms (0.9%)

Counts

12 → 216

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

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

54 calls:

Time	Variable		Point	Expression
23.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
17.0ms	cosTheta	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
9.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
6.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
5.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite467.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3576×	`-lowering-.f32`
3576×	`-lowering-.f64`
2852×	`/-lowering-/.f32`
2852×	`/-lowering-/.f64`
1848×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	99
1	158	96
2	1257	96
0	8991	96

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 995

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

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

simplify393.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

5948×	`-lowering-.f32`
5948×	`-lowering-.f64`
2560×	`/-lowering-/.f32`
2560×	`/-lowering-/.f64`
2314×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	4532
1	731	3703
2	2928	3619
0	8798	3619

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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))))
(/ -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 (PI))
(- (/ (pow alpha 2) (PI)) (/ 1 (PI)))
(- (/ (pow alpha 2) (PI)) (/ 1 (PI)))
(- (/ (pow alpha 2) (PI)) (/ 1 (PI)))
(/ (pow alpha 2) (PI))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(/ (pow alpha 2) (PI))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
-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)))
(* 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))
(* -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))
(* 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)))

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

eval159.0ms (1.7%)

Compiler: Compiled 64935 to 3716 computations (94.3% saved)

prune235.0ms (2.5%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	1498	33	1531
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1499	34	1533

Accuracy

99.9%

Counts

1533 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.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))))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	97.9%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	93.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.0%	(/.f32 (/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	97.9%	(/.f32 (/.f32 #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))))
	67.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
▶	67.9%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.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))))
✓	98.4%	(/.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))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 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))))
	98.1%	(/.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))))
	97.3%	(/.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 alpha #s(literal 1 binary32))) #s(literal -1 binary32)) (pow.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 alpha #s(literal -1 binary32))) #s(literal -1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.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))))
	67.9%	(/.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))))
	97.5%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 cosTheta (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))

Compiler

Compiled 2186 to 1125 computations (48.5% saved)

simplify11.0ms (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))) #s(literal -1 binary32))
✓	cost-diff	(/.f32 (+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32))
✓	cost-diff	(/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))
✓	cost-diff	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
✓	cost-diff	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	cost-diff	(/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
✓	cost-diff	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
✓	cost-diff	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	(.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
✓	cost-diff	(PI.f32)
✓	cost-diff	(/.f32 #s(literal -1 binary32) (PI.f32))
✓	cost-diff	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
✓	cost-diff	(+.f32 (*.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)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))))
✓	cost-diff	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	cost-diff	(.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (log.f32 alpha))))))
✓	cost-diff	(*.f32 alpha alpha)
✓	cost-diff	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha)))))))

Rules

36×	`-lowering-.f32`
36×	`-lowering-.f64`
26×	`/-lowering-/.f32`
26×	`/-lowering-/.f64`
14×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	576

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize229.0ms (2.5%)

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

Results

141.0ms

256×

invalid

Compiler

Compiled 579 to 50 computations (91.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 32.0ms (44.5% of total)

ival-div: 19.0ms (26.4% of total)

ival-add: 8.0ms (11.1% of total)

ival-log: 7.0ms (9.7% of total)

ival-sub: 4.0ms (5.6% of total)

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

const: 1.0ms (1.4% of total)

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

series93.0ms (1%)

Counts

26 → 384

Calls

Call 1

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

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

102 calls:

Time	Variable		Point	Expression
21.0ms	alpha	@	-inf	(* 2 (+ (* (log alpha) (* (PI) (- 1 (* cosTheta cosTheta)))) (* (* cosTheta cosTheta) (* (* alpha alpha) (* (PI) (log alpha))))))
8.0ms	alpha	@	-inf	(log alpha)
7.0ms	alpha	@	0	(log alpha)
4.0ms	alpha	@	inf	(log alpha)
4.0ms	cosTheta	@	0	(* 2 (+ (* (log alpha) (* (PI) (- 1 (* cosTheta cosTheta)))) (* (* cosTheta cosTheta) (* (* alpha alpha) (* (PI) (log alpha))))))

rewrite18.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

36×	`-lowering-.f32`
36×	`-lowering-.f64`
26×	`/-lowering-/.f32`
26×	`/-lowering-/.f64`
14×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	309

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify407.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

6486×	`-lowering-.f32`
6486×	`-lowering-.f64`
2960×	`+-lowering-+.f64`
2960×	`+-lowering-+.f32`
2028×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	774	9702
1	2754	8053
0	8588	8053

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

eval106.0ms (1.1%)

Compiler: Compiled 25626 to 901 computations (96.5% saved)

prune75.0ms (0.8%)

Pruning

34 alts after pruning (31 fresh and 3 done)

	Pruned	Kept	Total
New	723	16	739
Fresh	13	15	28
Picked	3	2	5
Done	0	1	1
Total	739	34	773

Accuracy

99.9%

Counts

773 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha))))))
	93.3%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
▶	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
	93.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	97.8%	(/.f32 (/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	83.7%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 0 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	87.7%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 alpha alpha) (+.f32 (-.f32 #s(literal 0 binary32) (.f32 alpha 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))))
	67.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
✓	67.9%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	65.6%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
▶	98.1%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
▶	97.1%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)))
✓	98.4%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha)))))))
	93.3%	(/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (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))))
	98.1%	(/.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))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	67.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
	97.5%	(+.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))

Compiler

Compiled 1767 to 1009 computations (42.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
22×	`-lowering-.f32`
22×	`-lowering-.f64`
6×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	417

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize175.0ms (1.9%)

Localize:

Found 20 expressions of interest:

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

Results

105.0ms

256×

invalid

Compiler

Compiled 420 to 38 computations (91% saved)

Precisions

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

ival-mult: 22.0ms (38.8% of total)

ival-div: 17.0ms (30% of total)

ival-log: 7.0ms (12.3% of total)

ival-sub: 5.0ms (8.8% of total)

ival-add: 4.0ms (7.1% of total)

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

const: 1.0ms (1.8% of total)

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

series99.0ms (1.1%)

Counts

20 → 264

Calls

Call 1

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

Calls

69 calls:

Time	Variable		Point	Expression
36.0ms	alpha	@	inf	(/ (- (/ (* alpha alpha) (PI)) (/ 1 (PI))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
30.0ms	alpha	@	0	(/ (/ (+ (* alpha alpha) -1) (PI)) (* (* (log alpha) 2) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
5.0ms	alpha	@	-inf	(* alpha (+ 1 (/ -1 (* alpha alpha))))
4.0ms	cosTheta	@	inf	(/ (/ (+ (* alpha alpha) -1) (PI)) (* (* (log alpha) 2) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
2.0ms	alpha	@	inf	(/ (/ (+ (* alpha alpha) -1) (PI)) (* (* (log alpha) 2) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite20.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
22×	`-lowering-.f32`
22×	`-lowering-.f64`
6×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	201

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

20 → 20

Calls

Call 1

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

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

simplify363.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

5608×	`-lowering-.f32`
5608×	`-lowering-.f64`
3174×	`/-lowering-/.f32`
3174×	`/-lowering-/.f64`
1686×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	6952
1	1566	5831
2	6972	5792
0	8303	5792

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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

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

eval40.0ms (0.4%)

Compiler: Compiled 16859 to 520 computations (96.9% saved)

prune51.0ms (0.5%)

Pruning

36 alts after pruning (31 fresh and 5 done)

	Pruned	Kept	Total
New	527	9	536
Fresh	4	22	26
Picked	3	2	5
Done	0	3	3
Total	534	36	570

Accuracy

100.0%

Counts

570 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha))))))
	93.3%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	93.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
▶	98.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	83.7%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 0 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	87.7%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (.f32 alpha alpha) (+.f32 (-.f32 #s(literal 0 binary32) (.f32 alpha 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))))
	67.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
▶	-0.0%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	67.9%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	65.6%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	96.9%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
✓	97.1%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)))
✓	98.4%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha)))))))
	93.3%	(/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
	98.1%	(/.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))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	93.6%	(/.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))))
	67.8%	(/.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 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.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 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	96.8%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) (neg.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)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
▶	95.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1777 to 1029 computations (42.1% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	425

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize191.0ms (2.1%)

Localize:

Found 20 expressions of interest:

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

Results

118.0ms

256×

invalid

Compiler

Compiled 428 to 47 computations (89% saved)

Precisions

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

ival-mult: 28.0ms (43.8% of total)

ival-div: 17.0ms (26.6% of total)

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

ival-log: 7.0ms (10.9% of total)

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

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

const: 1.0ms (1.6% of total)

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

series28.0ms (0.3%)

Counts

22 → 276

Calls

Call 1

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

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

69 calls:

Time	Variable		Point	Expression
6.0ms	alpha	@	inf	(/ (PI) (+ (* alpha alpha) -1))
1.0ms	alpha	@	-inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (* (* (log alpha) 2) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	cosTheta	@	inf	(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ -1 (* (PI) (* alpha alpha))))) (* (* (log alpha) 2) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	cosTheta	@	inf	(/ (* (+ alpha 1) (+ alpha -1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))

rewrite20.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	210

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

22 → 22

Calls

Call 1

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

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

simplify363.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

6104×	`-lowering-.f32`
6104×	`-lowering-.f64`
3230×	`/-lowering-/.f32`
3230×	`/-lowering-/.f64`
1788×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	483	7119
1	1729	5846
2	7662	5806
0	8359	5806

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

eval59.0ms (0.6%)

Compiler: Compiled 15321 to 518 computations (96.6% saved)

prune61.0ms (0.7%)

Pruning

35 alts after pruning (27 fresh and 8 done)

	Pruned	Kept	Total
New	454	5	459
Fresh	4	22	26
Picked	2	3	5
Done	0	5	5
Total	460	35	495

Accuracy

100.0%

Counts

495 → 35

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha))))))
	93.3%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	93.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
✓	98.3%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	83.7%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (-.f32 #s(literal 0 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	67.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
✓	-0.0%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
✓	67.9%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	65.6%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))))
✓	97.1%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32)))
✓	98.4%	(/.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))))
	93.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 (PI.f32) (log.f32 alpha)))))))
	98.1%	(/.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))))
	66.6%	(/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 (+.f32 #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 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	93.4%	(/.f32 (.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (*.f32 alpha alpha))))) (log.f32 alpha))
	98.1%	(/.f32 (.f32 (.f32 alpha alpha) (/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) alpha) alpha)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	93.6%	(/.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))))
	67.8%	(/.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 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))) (/.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 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	96.8%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) (neg.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)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))
✓	95.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 2647 to 796 computations (69.9% saved)

regimes86.0ms (0.9%)

Counts

65 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

20.0ms	alpha
19.0ms	(*.f32 alpha alpha)
19.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
18.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`alpha`
98.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes104.0ms (1.1%)

Counts

58 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

50.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
19.0ms	alpha
16.0ms	(*.f32 alpha alpha)
15.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta`
98.4%	1	`alpha`
98.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
98.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes119.0ms (1.3%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

102.0ms	(*.f32 alpha alpha)
7.0ms	alpha
7.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes30.0ms (0.3%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

3 calls:

18.0ms	(*.f32 alpha alpha)
5.0ms	alpha
5.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes38.0ms (0.4%)

Counts

16 → 1

Calls

Call 1

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

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:

26.0ms	alpha
5.0ms	(*.f32 alpha alpha)
5.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes21.0ms (0.2%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes16.0ms (0.2%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	cosTheta
5.0ms	alpha
5.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
93.7%	1	`cosTheta`
93.7%	1	`alpha`
93.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
67.8%	1	`cosTheta`
67.8%	1	`alpha`
67.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
65.6%	1	`alpha`
65.6%	1	`(*.f32 alpha alpha)`
65.6%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

48×	`*-commutative_binary32`
16×	`+-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	54	166
1	89	166
2	96	166
3	103	166
4	104	166

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.1s (22.3%)

Rules

6486×	`-lowering-.f32`
6486×	`-lowering-.f64`
5948×	`-lowering-.f32`
5948×	`-lowering-.f64`
5608×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	224	4532
1	731	3703
2	2928	3619
0	8798	3619
0	21	99
1	158	96
2	1257	96
0	8991	96
0	13	21
1	44	19
2	160	19
3	684	19
4	2882	19
5	6032	19
0	8041	19
0	774	9702
1	2754	8053
0	8588	8053
0	445	6952
1	1566	5831
2	6972	5792
0	8303	5792

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 361 to 190 computations (47.4% saved)

preprocess83.0ms (0.9%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1576 to 810 computations (48.6% saved)

analyze90.0ms (1%)

sample1.7s (18.7%)

preprocess224.0ms (2.4%)

explain441.0ms (4.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify174.0ms (1.9%)

localize204.0ms (2.2%)

series82.0ms (0.9%)

rewrite467.0ms (5.1%)

simplify393.0ms (4.3%)

eval159.0ms (1.7%)

prune235.0ms (2.5%)

simplify11.0ms (0.1%)

localize229.0ms (2.5%)

series93.0ms (1%)

rewrite18.0ms (0.2%)

simplify407.0ms (4.4%)

eval106.0ms (1.1%)

prune75.0ms (0.8%)

simplify11.0ms (0.1%)

localize175.0ms (1.9%)

series99.0ms (1.1%)

rewrite20.0ms (0.2%)

simplify363.0ms (3.9%)

eval40.0ms (0.4%)

prune51.0ms (0.5%)

simplify11.0ms (0.1%)

localize191.0ms (2.1%)

series28.0ms (0.3%)

rewrite20.0ms (0.2%)

simplify363.0ms (3.9%)

eval59.0ms (0.6%)

prune61.0ms (0.7%)

regimes86.0ms (0.9%)

regimes104.0ms (1.1%)

regimes119.0ms (1.3%)

regimes30.0ms (0.3%)

regimes38.0ms (0.4%)

regimes21.0ms (0.2%)

regimes16.0ms (0.2%)

regimes9.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

simplify12.0ms (0.1%)

soundness2.1s (22.3%)

preprocess83.0ms (0.9%)

end0.0ms (0%)

Profiling