Metrics for GTR1 distribution

analyze123.0ms (1.2%)

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: 86.0ms

ival-mult: 45.0ms (52.5% of total)

ival-sub: 10.0ms (11.7% of total)

...c/correct-round.rkt:119:19: 8.0ms (9.3% of total)

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

ival-<=: 6.0ms (7% of total)

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

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

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

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

const: 1.0ms (1.2% of total)

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

sample2.1s (20.3%)

Results

1.7s

8256×

valid

Precisions

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

ival-<=: 391.0ms (29.1% of total)

ival-mult: 332.0ms (24.7% of total)

...c/correct-round.rkt:119:19: 171.0ms (12.7% of total)

ival-log: 149.0ms (11.1% of total)

ival-add: 71.0ms (5.3% of total)

ival-div: 70.0ms (5.2% of total)

ival-sub: 70.0ms (5.2% of total)

ival-and: 40.0ms (3% of total)

ival-pi: 36.0ms (2.7% of total)

const: 12.0ms (0.9% of total)

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

Bogosity

preprocess216.0ms (2.1%)

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)

explain167.0ms (1.6%)

FPErrors

Click to see full error table

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

Results

98.0ms

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: 16.0ms (40.2% of total)

ival-div: 8.0ms (20.1% of total)

ival-log: 7.0ms (17.6% 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
▶	98.4%	(/.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

▶

98.4%

(/.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)

simplify165.0ms (1.6%)

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

localize128.0ms (1.3%)

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	98.9%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.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	99.6%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

88.0ms

256×

valid

Compiler

Compiled 181 to 22 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 13.0ms (43.6% of total)

ival-div: 6.0ms (20.1% of total)

ival-log: 4.0ms (13.4% of total)

ival-add: 4.0ms (13.4% of total)

ival-pi: 1.0ms (3.4% of total)

ival-sub: 1.0ms (3.4% of total)

const: 1.0ms (3.4% of total)

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

series69.0ms (0.7%)

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)))
11.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
7.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
4.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
4.0ms	alpha	@	inf	(/ (+ (* alpha alpha) -1) (PI))

rewrite416.0ms (4.1%)

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	8992	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 alpha alpha) #s(literal -1 binary32)) (.f32 (.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 alpha alpha) (.f32 (.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 1 binary32) (.f32 (.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 (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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 (.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 #s(literal 1 binary32) (.f32 (.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 (.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 #s(literal 1 binary32) (.f32 (.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 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)))))) #s(literal 1 binary32)) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)))))) (.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 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)))))) (.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 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 cosTheta cosTheta) (*.f32 cosTheta cosTheta)))))) #s(literal 1 binary32)))
(+.f32 (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))) (+.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.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 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 cosTheta cosTheta) (.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 (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 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 #s(literal 1 binary32) (.f32 (.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 alpha alpha) #s(literal -1 binary32)) (.f32 (.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 alpha alpha) (.f32 (.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 1 binary32) (.f32 (.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 (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 alpha alpha) #s(literal -1 binary32)) (.f32 (.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 alpha alpha) #s(literal -1 binary32)) (.f32 (.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 (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 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.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 (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.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 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.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 alpha (.f32 alpha (.f32 alpha alpha)))) (.f32 (.f32 (.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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (*.f32 alpha alpha) #s(literal 1 binary32))))))
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(.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)))

simplify341.0ms (3.3%)

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 #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 (* (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))

eval151.0ms (1.5%)

Compiler: Compiled 64979 to 3720 computations (94.3% saved)

prune219.0ms (2.1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	1503	28	1531
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1504	29	1533

Accuracy

99.9%

Counts

1533 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (/.f32 (/.f32 (-.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 #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)))))
	98.2%	(/.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)))
	98.1%	(/.f32 (/.f32 (-.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 (.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 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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.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)))))
	97.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
▶	98.4%	(/.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 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	95.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	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))))
	66.7%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	66.7%	(/.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)))))
	98.2%	(/.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)))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.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))))
▶	97.3%	(/.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))))
	47.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	98.4%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.1%	(/.f32 (.f32 (+.f32 alpha #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) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.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))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	66.7%	(/.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 1950 to 915 computations (53.1% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	474

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize291.0ms (2.8%)

Localize:

Found 20 expressions of interest:

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

Results

194.0ms

256×

invalid

Compiler

Compiled 477 to 45 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 27.0ms (41.3% of total)

ival-div: 14.0ms (21.4% of total)

ival-add: 14.0ms (21.4% of total)

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

ival-neg: 3.0ms (4.6% of total)

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

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

const: 1.0ms (1.5% of total)

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

series36.0ms (0.4%)

Counts

24 → 360

Calls

Call 1

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

96 calls:

Time	Variable		Point	Expression
5.0ms	alpha	@	inf	(* (+ alpha 1) (/ (+ alpha -1) (PI)))
2.0ms	cosTheta	@	inf	(/ (* (+ alpha 1) (/ (+ alpha -1) (PI))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
2.0ms	cosTheta	@	inf	(/ (+ (* (+ alpha -1) alpha) (* (+ alpha -1) 1)) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	-inf	(/ (* (+ alpha 1) (/ (+ alpha -1) (PI))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))

rewrite22.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	242

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

24 → 24

Calls

Call 1

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

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

simplify343.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

5136×	`-lowering-.f32`
5136×	`-lowering-.f64`
3182×	`/-lowering-/.f32`
3182×	`/-lowering-/.f64`
2378×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	516	8935
1	1775	7294
2	7588	7233
0	8239	7233

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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))))))))
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alpha
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(* 2 (* (PI) (log alpha)))
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(.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)))

eval50.0ms (0.5%)

Compiler: Compiled 22402 to 712 computations (96.8% saved)

prune53.0ms (0.5%)

Pruning

36 alts after pruning (34 fresh and 2 done)

	Pruned	Kept	Total
New	683	16	699
Fresh	5	18	23
Picked	4	1	5
Done	0	1	1
Total	692	36	728

Accuracy

99.9%

Counts

728 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (/.f32 (/.f32 (-.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 #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)))))
	98.2%	(/.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)))))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha)))
	98.1%	(/.f32 (/.f32 (-.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 (.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 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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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)))))
▶	98.4%	(/.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 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
✓	98.4%	(/.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 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	97.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
▶	-0.0%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (*.f32 alpha alpha)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	95.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	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))))
	66.7%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	66.7%	(/.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)))))
	98.2%	(/.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)))))
	98.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	97.3%	(/.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))))
	46.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	47.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
▶	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.1%	(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.1%	(/.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 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) 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)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 alpha 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)))))
	97.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.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))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	66.7%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.0%	(+.f32 (/.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	96.8%	(+.f32 (neg.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (/.f32 (.f32 alpha (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
▶	96.5%	(.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))

Compiler

Compiled 2208 to 1097 computations (50.3% saved)

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	435

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize248.0ms (2.4%)

Localize:

Found 20 expressions of interest:

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

Results

170.0ms

256×

invalid

Compiler

Compiled 438 to 48 computations (89% saved)

Precisions

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

ival-mult: 28.0ms (43.6% of total)

ival-div: 14.0ms (21.8% of total)

ival-add: 12.0ms (18.7% 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)

series73.0ms (0.7%)

Counts

23 → 300

Calls

Call 1

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

Calls

78 calls:

Time	Variable		Point	Expression
31.0ms	alpha	@	0	(log alpha)
12.0ms	alpha	@	-inf	(log alpha)
6.0ms	alpha	@	inf	(log alpha)
2.0ms	alpha	@	-inf	(/ (/ (+ (* alpha alpha) -1) (PI)) (* (* (log alpha) 2) (+ 1 (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta))))
2.0ms	alpha	@	inf	(/ (/ (+ (* alpha alpha) -1) (PI)) (* (* (log alpha) 2) (+ 1 (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta))))

rewrite28.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	216

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 23

Calls

Call 1

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

simplify328.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

5542×	`-lowering-.f32`
5542×	`-lowering-.f64`
3558×	`/-lowering-/.f32`
3558×	`/-lowering-/.f64`
2200×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	484	6717
1	1730	5473
2	7583	5449
0	8215	5449

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

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

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

eval59.0ms (0.6%)

Compiler: Compiled 15884 to 605 computations (96.2% saved)

prune109.0ms (1.1%)

Pruning

44 alts after pruning (40 fresh and 4 done)

	Pruned	Kept	Total
New	503	19	522
Fresh	8	21	29
Picked	3	2	5
Done	0	2	2
Total	514	44	558

Accuracy

100.0%

Counts

558 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.3%	(/.f32 (/.f32 (/.f32 (-.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 #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)))))
	98.2%	(/.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)))))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (log.f32 alpha)) (*.f32 cosTheta cosTheta))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (neg.f32 (log.f32 alpha)))
▶	66.7%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
	98.1%	(/.f32 (/.f32 (-.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 (.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 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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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)))))
	97.3%	(/.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 (neg.f32 cosTheta) cosTheta))))
✓	98.4%	(/.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 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	95.2%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	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))))
	1.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
	66.7%	(/.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)))
	66.7%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	98.2%	(/.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)))))
	97.3%	(/.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)))))
✓	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))))
	46.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	47.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
▶	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.1%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
✓	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.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 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) 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)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.0%	(/.f32 (.f32 (.f32 alpha 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)))))
	94.7%	(/.f32 (.f32 alpha (+.f32 (+.f32 alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	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))))
	95.1%	(/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32))) (log.f32 alpha))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	66.7%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	96.3%	(-.f32 (.f32 (/.f32 alpha (PI.f32)) (+.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha)) (log.f32 (.f32 alpha alpha))))) (/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) (+.f32 (+.f32 alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	96.2%	(+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (PI.f32)) (log.f32 alpha)) (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
	96.5%	(.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
✓	96.5%	(.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.3%	(.f32 (/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	66.1%	(.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.1%	(.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))))) (log.f32 (.f32 alpha alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	47.2%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))))
	95.8%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (PI.f32)) (neg.f32 (log.f32 alpha))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))

Compiler

Compiled 2422 to 1277 computations (47.3% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	688

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize426.0ms (4.2%)

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

Results

329.0ms

256×

invalid

Compiler

Compiled 691 to 51 computations (92.6% saved)

Precisions

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

ival-mult: 26.0ms (35.5% of total)

ival-div: 25.0ms (34.1% of total)

ival-add: 10.0ms (13.7% of total)

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

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

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

const: 1.0ms (1.4% of total)

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

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

series62.0ms (0.6%)

Counts

25 → 288

Calls

Call 1

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

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

Calls

72 calls:

Time	Variable		Point	Expression
18.0ms	alpha	@	inf	(/ (* (* alpha alpha) (+ (/ 1 (PI)) (/ (/ -1 (* alpha alpha)) (PI)))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
6.0ms	alpha	@	inf	(/ (/ (/ (- (* (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (/ 1 (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (+ (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (PI)) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
3.0ms	cosTheta	@	0	(/ (/ (/ (- (* (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (/ 1 (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (+ (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (PI)) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
3.0ms	alpha	@	0	(/ (/ (/ (- (* (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (/ 1 (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (+ (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (PI)) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
3.0ms	cosTheta	@	inf	(/ (/ (/ (- (* (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1))) (* (/ 1 (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (+ (/ (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (/ 1 (+ (* alpha alpha) 1)))) (PI)) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite24.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	420

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

25 → 25

Calls

Call 1

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

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

simplify402.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

5968×	`-lowering-.f32`
5968×	`-lowering-.f64`
4064×	`/-lowering-/.f32`
4064×	`/-lowering-/.f64`
3126×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	8593
1	2039	7163
0	8562	7163

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

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

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

eval137.0ms (1.3%)

Compiler: Compiled 33607 to 686 computations (98% saved)

prune95.0ms (0.9%)

Pruning

39 alts after pruning (30 fresh and 9 done)

	Pruned	Kept	Total
New	597	7	604
Fresh	12	23	35
Picked	0	5	5
Done	0	4	4
Total	609	39	648

Accuracy

100.0%

Counts

648 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.3%	(/.f32 (/.f32 (/.f32 (-.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 #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)))))
	98.2%	(/.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)))))
✓	66.7%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
	36.0%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (.f32 (.f32 (+.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal -1 binary32)) cosTheta) cosTheta))
	98.1%	(/.f32 (/.f32 (-.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 (.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 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 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (+.f32 (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.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)))))
	97.3%	(/.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 (neg.f32 cosTheta) cosTheta))))
✓	98.4%	(/.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 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	95.2%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	65.5%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))
✓	-0.0%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	66.7%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) cosTheta))))
	95.0%	(/.f32 (-.f32 (/.f32 (pow.f32 alpha #s(literal 8 binary32)) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))))
	98.2%	(/.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)))))
	97.3%	(/.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)))))
✓	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))))
	46.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	47.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	95.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
✓	97.3%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
✓	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	97.1%	(/.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 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) 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 (.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)))))
	94.7%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
	94.7%	(/.f32 (.f32 alpha (+.f32 (+.f32 alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.0%	(/.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 (neg.f32 cosTheta) cosTheta))))
	95.1%	(/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32))) (log.f32 alpha))
	66.7%	(/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 (PI.f32) (log.f32 alpha))))
	96.3%	(-.f32 (.f32 (/.f32 alpha (PI.f32)) (+.f32 (/.f32 (+.f32 alpha #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha)) (log.f32 (.f32 alpha alpha))))) (/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) alpha) (+.f32 (+.f32 alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	96.2%	(+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (PI.f32)) (log.f32 alpha)) (.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))))
	96.5%	(.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
✓	96.5%	(.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.3%	(.f32 (/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	66.1%	(.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	47.2%	(.f32 (.f32 cosTheta cosTheta) (-.f32 (+.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))))
	95.8%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1/2 binary32) (.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta))) (PI.f32)) (neg.f32 (log.f32 alpha))) (.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha)) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))

Compiler

Compiled 3099 to 916 computations (70.4% saved)

regimes117.0ms (1.1%)

Counts

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

Outputs

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

Calls

4 calls:

49.0ms	(/.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))))
21.0ms	cosTheta
21.0ms	alpha
21.0ms	(*.f32 alpha alpha)

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)

regimes50.0ms (0.5%)

Counts

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

Outputs

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

Calls

4 calls:

12.0ms	(*.f32 alpha alpha)
12.0ms	(/.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))))
11.0ms	cosTheta
11.0ms	alpha

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)

regimes69.0ms (0.7%)

Counts

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

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:

33.0ms	cosTheta
13.0ms	(*.f32 alpha alpha)
10.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
10.0ms	alpha

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)

regimes51.0ms (0.5%)

Counts

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

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 (neg.f32 cosTheta) cosTheta))))

Calls

3 calls:

28.0ms	alpha
10.0ms	(*.f32 alpha alpha)
10.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.3%	1	`cosTheta`
97.3%	1	`alpha`
97.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes41.0ms (0.4%)

Counts

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

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

Calls

3 calls:

20.0ms	alpha
8.0ms	(*.f32 alpha alpha)
8.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.3%	1	`cosTheta`
97.3%	1	`alpha`
97.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes26.0ms (0.3%)

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`cosTheta`
97.3%	1	`alpha`
97.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes25.0ms (0.2%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.3%	1	`cosTheta`
97.3%	1	`alpha`
97.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes23.0ms (0.2%)

Counts

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

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

Calls

3 calls:

8.0ms	alpha
7.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`alpha`
96.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes48.0ms (0.5%)

Counts

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

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

Calls

3 calls:

34.0ms	cosTheta
7.0ms	(*.f32 alpha alpha)
6.0ms	alpha

Results

Accuracy	Segments	Branch
96.5%	1	`cosTheta`
96.5%	1	`alpha`
96.5%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes19.0ms (0.2%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.2%	1	`cosTheta`
95.2%	1	`alpha`
95.2%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes18.0ms (0.2%)

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.1%	1	`cosTheta`
95.1%	1	`alpha`
95.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes97.0ms (0.9%)

Counts

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

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

Calls

3 calls:

88.0ms	(*.f32 alpha alpha)
4.0ms	alpha
4.0ms	cosTheta

Results

Accuracy	Segments	Branch
66.7%	1	`cosTheta`
66.7%	1	`alpha`
66.7%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes12.0ms (0.1%)

Counts

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

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

Calls

3 calls:

4.0ms	cosTheta
3.0ms	alpha
3.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
66.1%	1	`cosTheta`
66.1%	1	`alpha`
66.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
65.5%	1	`cosTheta`
65.5%	1	`alpha`
65.5%	1	`(*.f32 alpha alpha)`

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 #s(literal -1 binary32) (*.f32 alpha alpha)) (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)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

52×	`*-commutative_binary32`
22×	`+-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	68	245
1	112	245
2	119	245
3	128	245
4	129	245

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.6s (25.6%)

Rules

5968×	`-lowering-.f32`
5968×	`-lowering-.f64`
5948×	`-lowering-.f32`
5948×	`-lowering-.f64`
5542×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	8935
1	1775	7294
2	7588	7233
0	8239	7233
0	224	4532
1	731	3703
2	2928	3619
0	8798	3619
0	588	8593
1	2039	7163
0	8562	7163
0	21	99
1	158	96
2	1257	96
0	8992	96
0	13	21
1	44	19
2	160	19
3	684	19
4	2882	19
5	6032	19
0	8041	19
0	484	6717
1	1730	5473
2	7583	5449
0	8215	5449

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
1×	iter limit
1×	node limit

Compiler

Compiled 869 to 462 computations (46.8% saved)

preprocess85.0ms (0.8%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1898 to 976 computations (48.6% saved)

analyze123.0ms (1.2%)

sample2.1s (20.3%)

preprocess216.0ms (2.1%)

explain167.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify165.0ms (1.6%)

localize128.0ms (1.3%)

series69.0ms (0.7%)

rewrite416.0ms (4.1%)

simplify341.0ms (3.3%)

eval151.0ms (1.5%)

prune219.0ms (2.1%)

simplify13.0ms (0.1%)

localize291.0ms (2.8%)

series36.0ms (0.4%)

rewrite22.0ms (0.2%)

simplify343.0ms (3.3%)

eval50.0ms (0.5%)

prune53.0ms (0.5%)

simplify25.0ms (0.2%)

localize248.0ms (2.4%)

series73.0ms (0.7%)

rewrite28.0ms (0.3%)

simplify328.0ms (3.2%)

eval59.0ms (0.6%)

prune109.0ms (1.1%)

simplify15.0ms (0.2%)

localize426.0ms (4.2%)

series62.0ms (0.6%)

rewrite24.0ms (0.2%)

simplify402.0ms (3.9%)

eval137.0ms (1.3%)

prune95.0ms (0.9%)

regimes117.0ms (1.1%)

regimes50.0ms (0.5%)

regimes69.0ms (0.7%)

regimes51.0ms (0.5%)

regimes41.0ms (0.4%)

regimes26.0ms (0.3%)

regimes25.0ms (0.2%)

regimes23.0ms (0.2%)

regimes48.0ms (0.5%)

regimes19.0ms (0.2%)

regimes18.0ms (0.2%)

regimes97.0ms (0.9%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

simplify11.0ms (0.1%)

soundness2.6s (25.6%)

preprocess85.0ms (0.8%)

end0.0ms (0%)

Profiling