Metrics for GTR1 distribution

analyze87.0ms (0.8%)

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: 53.0ms

ival-mult: 19.0ms (35.6% of total)

...c/correct-round.rkt:119:19: 8.0ms (15% of total)

ival-<=: 8.0ms (15% of total)

ival-log: 6.0ms (11.2% of total)

ival-div: 3.0ms (5.6% of total)

ival-sub: 3.0ms (5.6% of total)

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

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

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

const: 1.0ms (1.9% of total)

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

sample2.1s (19.4%)

Results

1.6s

8256×

valid

Precisions

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

ival-<=: 372.0ms (29.1% of total)

ival-mult: 354.0ms (27.7% of total)

...c/correct-round.rkt:119:19: 168.0ms (13.1% of total)

ival-log: 118.0ms (9.2% of total)

ival-div: 74.0ms (5.8% of total)

ival-sub: 61.0ms (4.8% of total)

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

ival-pi: 38.0ms (3% of total)

ival-and: 37.0ms (2.9% of total)

const: 11.0ms (0.9% of total)

backward-pass: 4.0ms (0.3% of total)

Bogosity

preprocess223.0ms (2%)

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)

explain190.0ms (1.7%)

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

89.0ms

512×

valid

Compiler

Compiled 214 to 41 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 18.0ms (49.3% of total)

ival-log: 7.0ms (19.2% of total)

ival-div: 4.0ms (11% of total)

ival-sub: 3.0ms (8.2% of total)

ival-add: 3.0ms (8.2% of total)

ival-pi: 2.0ms (5.5% of total)

const: 1.0ms (2.7% 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)))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.4%

(/.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)))))

▶

98.6%

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

Compiler

Compiled 52 to 27 computations (48.1% saved)

simplify195.0ms (1.8%)

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

localize116.0ms (1.1%)

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	99.0%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	99.6%	(.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	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.9%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

79.0ms

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: 15.0ms (49.7% of total)

ival-div: 5.0ms (16.6% of total)

ival-add: 4.0ms (13.2% of total)

ival-log: 3.0ms (9.9% of total)

ival-pi: 1.0ms (3.3% of total)

ival-sub: 1.0ms (3.3% of total)

const: 1.0ms (3.3% of total)

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

series103.0ms (0.9%)

Counts

12 → 216

Calls

Call 1

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

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

54 calls:

Time	Variable		Point	Expression
61.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
8.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
5.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
4.0ms	alpha	@	inf	(/ (+ (* alpha alpha) -1) (PI))

rewrite467.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 995

Calls

Call 1

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

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

simplify325.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval173.0ms (1.6%)

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

prune223.0ms (2%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	1501	30	1531
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	1501	32	1533

Accuracy

99.9%

Counts

1533 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) #s(literal 3 binary32))) (+.f32 (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (+.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))))))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (-.f32 (.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 #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))))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #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) #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)))))
	96.7%	(/.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 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	95.2%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.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)))))
▶	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	64.4%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
▶	64.4%	(/.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 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
	96.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	48.0%	(/.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))))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.4%	(/.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))))
	98.0%	(/.f32 (.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (+.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)))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.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))))
	97.9%	(+.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (.f32 cosTheta cosTheta) (-.f32 (/.f32 (/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (log.f32 (.f32 alpha alpha))) (PI.f32)) (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) #s(literal 4 binary32)) (PI.f32))))) (.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))))))
	97.0%	(+.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 2068 to 1039 computations (49.8% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	555

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize271.0ms (2.5%)

Localize:

Found 20 expressions of interest:

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

Results

191.0ms

256×

invalid

Compiler

Compiled 558 to 44 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-div: 32.0ms (45.4% of total)

ival-mult: 21.0ms (29.8% of total)

ival-add: 10.0ms (14.2% of total)

ival-log: 4.0ms (5.7% of total)

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

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

const: 1.0ms (1.4% of total)

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

series38.0ms (0.3%)

Counts

26 → 372

Calls

Call 1

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

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

Calls

99 calls:

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

rewrite23.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	295

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify354.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

6516×	`-lowering-.f32`
6516×	`-lowering-.f64`
2928×	`+-lowering-+.f64`
2928×	`+-lowering-+.f32`
2210×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	670	10085
1	2295	8225
0	8433	8225

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

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

eval54.0ms (0.5%)

Compiler: Compiled 25577 to 833 computations (96.7% saved)

prune59.0ms (0.5%)

Pruning

38 alts after pruning (33 fresh and 5 done)

	Pruned	Kept	Total
New	698	15	713
Fresh	7	18	25
Picked	2	3	5
Done	0	2	2
Total	707	38	745

Accuracy

100.0%

Counts

745 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(/.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 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
▶	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))
	94.8%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 (/.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
▶	79.8%	(/.f32 (/.f32 (/.f32 #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)))))
	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 #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))))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #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) #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)))))
	96.7%	(/.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 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	95.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.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)))))
✓	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	80.0%	(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	64.4%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
✓	64.4%	(/.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)))))
	64.4%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))))
	64.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (neg.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))))
	96.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	96.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	48.0%	(/.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))))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	95.0%	(/.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))))
	95.4%	(/.f32 (+.f32 (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.4%	(/.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))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.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 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))
	97.0%	(+.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 1970 to 1136 computations (42.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	509

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize310.0ms (2.8%)

Localize:

Found 20 expressions of interest:

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

Results

231.0ms

256×

invalid

Compiler

Compiled 512 to 51 computations (90% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 24.0ms (35.3% of total)

ival-div: 19.0ms (28% of total)

ival-add: 10.0ms (14.7% of total)

ival-log: 7.0ms (10.3% of total)

ival-sub: 5.0ms (7.4% of total)

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

const: 1.0ms (1.5% of total)

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

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

series128.0ms (1.2%)

Counts

26 → 336

Calls

Call 1

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

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

Calls

87 calls:

Time	Variable		Point	Expression
33.0ms	cosTheta	@	0	(/ (/ (/ (+ (* alpha (* alpha (* alpha alpha))) -1) (PI)) (+ (* alpha alpha) 1)) (* 2 (* (log alpha) (+ (- 1 (* cosTheta cosTheta)) (* alpha (* alpha (* cosTheta cosTheta)))))))
22.0ms	cosTheta	@	0	(* 2 (* (log alpha) (+ (- 1 (* cosTheta cosTheta)) (* alpha (* alpha (* cosTheta cosTheta))))))
19.0ms	alpha	@	-inf	(log alpha)
6.0ms	alpha	@	inf	(log alpha)
6.0ms	alpha	@	0	(log alpha)

rewrite18.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	277

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify423.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

7162×	`-lowering-.f32`
7162×	`-lowering-.f64`
3250×	`+-lowering-+.f64`
3250×	`+-lowering-+.f32`
1690×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	657	8534
1	2461	6970
0	9103	6970

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

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

eval67.0ms (0.6%)

Compiler: Compiled 21162 to 709 computations (96.6% saved)

prune68.0ms (0.6%)

Pruning

38 alts after pruning (32 fresh and 6 done)

	Pruned	Kept	Total
New	587	13	600
Fresh	9	19	28
Picked	4	1	5
Done	0	5	5
Total	600	38	638

Accuracy

100.0%

Counts

638 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.8%	(/.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 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
	94.8%	(/.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 alpha) #s(literal 2 binary32)))
	94.8%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (log.f32 (*.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 (/.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (pow.f32 alpha #s(literal 4 binary32))))) (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 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	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)))))
	96.7%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	96.7%	(/.f32 (/.f32 (+.f32 (.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 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))))
	95.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.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)))))
✓	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	80.0%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	64.4%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
✓	64.4%	(/.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)))))
	78.7%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
▶	64.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	96.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
▶	96.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	46.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	95.0%	(/.f32 (+.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1/2 binary32)) #s(literal -1/2 binary32)) (.f32 (log.f32 alpha) (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))))
	95.4%	(/.f32 (+.f32 (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal 1 binary32)) #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	98.4%	(/.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))))
	98.2%	(/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha))) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.4%	(/.f32 (.f32 alpha (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	64.3%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	96.6%	(+.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (PI.f32)))))
	97.0%	(+.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)))))
	96.5%	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.1%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))))

Compiler

Compiled 1833 to 1078 computations (41.2% saved)

simplify369.0ms (3.4%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
✓	cost-diff	64	(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
✓	cost-diff	320	(/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))
✓	cost-diff	0	(*.f32 alpha alpha)
✓	cost-diff	0	(-.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
✓	cost-diff	0	(/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	cost-diff	0	(.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32)))
✓	cost-diff	0	(*.f32 alpha alpha)
✓	cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	cost-diff	0	(log.f32 (*.f32 alpha alpha))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(/.f32 #s(literal -1 binary32) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓	cost-diff	0	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))))
✓	cost-diff	64	(+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))))

Rules

4852×	`-lowering-.f32`
4852×	`-lowering-.f64`
2732×	`/-lowering-/.f32`
2732×	`/-lowering-/.f64`
1836×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	394
1	166	382
2	657	374
3	3458	367
0	8361	367

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize412.0ms (3.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.0%	(.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha))))
✓	accuracy	98.9%	(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))))
✓	accuracy	98.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (PI.f32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))
✓	accuracy	98.8%	(/.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 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (neg.f32 (log.f32 alpha)) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))))
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.9%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	98.7%	(/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (*.f32 alpha alpha)))
✓	accuracy	99.9%	(.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
✓	accuracy	99.8%	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	accuracy	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	accuracy	98.9%	(.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32)))
✓	accuracy	100.0%	(*.f32 alpha alpha)
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	98.5%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓	accuracy	99.7%	(.f32 alpha (.f32 cosTheta cosTheta))
✓	accuracy	99.6%	(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
✓	accuracy	99.0%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))))

Results

274.0ms

256×

valid

Compiler

Compiled 494 to 49 computations (90.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-div: 34.0ms (40.3% of total)

ival-mult: 30.0ms (35.6% of total)

ival-add: 7.0ms (8.3% of total)

ival-log: 7.0ms (8.3% of total)

ival-sub: 4.0ms (4.7% of total)

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

const: 1.0ms (1.2% of total)

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

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

series53.0ms (0.5%)

Counts

25 → 420

Calls

Call 1

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

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

Calls

105 calls:

Time	Variable		Point	Expression
19.0ms	cosTheta	@	0	(/ (/ (/ (+ (* alpha (* alpha (* alpha alpha))) -1) (PI)) (+ (* alpha alpha) 1)) (* (* (* alpha alpha) -2) (* (neg (log alpha)) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
2.0ms	cosTheta	@	inf	(/ (/ (/ (+ (* alpha (* alpha (* alpha alpha))) -1) (PI)) (+ (* alpha alpha) 1)) (* (* (* alpha alpha) -2) (* (neg (log alpha)) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha))))))
1.0ms	alpha	@	inf	(/ (/ (+ (* alpha alpha) -1) (PI)) (* 2 (* (log alpha) (+ (- 1 (* cosTheta cosTheta)) (* alpha (* alpha (* cosTheta cosTheta)))))))
1.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
1.0ms	cosTheta	@	0	(* (* (* alpha alpha) -2) (* (neg (log alpha)) (+ (* cosTheta cosTheta) (/ (- 1 (* cosTheta cosTheta)) (* alpha alpha)))))

rewrite430.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3348×	`-lowering-.f32`
3348×	`-lowering-.f64`
2760×	`fma-lowering-fma.f32`
2760×	`fma-lowering-fma.f64`
1778×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	48	226
1	347	214
2	3382	213
0	8190	213

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 739

Calls

Call 1

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

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

simplify432.0ms (4%)

Algorithm

1×	egg-herbie

Rules

8558×	`-lowering-.f32`
8558×	`-lowering-.f64`
2638×	`+-lowering-+.f64`
2638×	`+-lowering-+.f32`
1772×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	693	8997
1	2518	7405
0	9122	7405

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

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

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

eval147.0ms (1.3%)

Compiler: Compiled 51409 to 3600 computations (93% saved)

prune305.0ms (2.8%)

Pruning

40 alts after pruning (33 fresh and 7 done)

	Pruned	Kept	Total
New	1502	24	1526
Fresh	18	9	27
Picked	2	3	5
Done	2	4	6
Total	1524	40	1564

Accuracy

100.0%

Counts

1564 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.8%	(/.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 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (/.f32 (.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 alpha (.f32 alpha alpha)))))) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 cosTheta cosTheta))) (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)) (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))))
	94.8%	(/.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 alpha) #s(literal 2 binary32)))
	98.2%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) #s(literal 2 binary32))) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))) (log.f32 alpha))
	98.2%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha))))
✓	-0.0%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	96.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) #s(literal 2 binary32))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
	96.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) #s(literal 2 binary32))))
✓	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)))))
✓	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))))))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (.f32 (.f32 alpha alpha) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))))))
	95.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 #s(literal 2 binary32) (*.f32 (log.f32 alpha) #s(literal 1 binary32))))
	95.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	79.8%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	98.3%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha))) (log.f32 alpha))) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
	64.4%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	64.0%	(/.f32 (/.f32 #s(literal -1 binary32) (*.f32 #s(literal 2 binary32) (log.f32 alpha))) (PI.f32))
✓	64.4%	(/.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)))))
	78.7%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
✓	64.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	96.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
✓	96.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 alpha) (*.f32 (PI.f32) #s(literal 2 binary32))))
	95.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	95.4%	(/.f32 (+.f32 (.f32 (+.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32)) alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	96.3%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
	96.4%	(/.f32 #s(literal 1 binary32) (/.f32 (.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)) (log.f32 alpha)))))
	64.1%	(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 #s(literal 2 binary32) (log.f32 alpha)) (/.f32 #s(literal -1 binary32) (PI.f32))))
	80.0%	(/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (.f32 #s(literal 2 binary32) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))))))
	98.0%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 (.f32 #s(literal -2 binary32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha)))) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (/.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))))))
	96.6%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))))
	64.0%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	64.3%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	96.5%	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.6%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) #s(literal 2 binary32))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
	96.5%	(.f32 (/.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 2 binary32)))
	96.4%	(.f32 (/.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (PI.f32) #s(literal 2 binary32))))
	96.3%	(.f32 (/.f32 (+.f32 #s(literal 1 binary32) alpha) (.f32 (PI.f32) #s(literal 2 binary32))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	64.0%	(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 #s(literal -2 binary32) (log.f32 alpha))))
	96.6%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 3150 to 941 computations (70.1% saved)

regimes387.0ms (3.5%)

Counts

84 → 1

Calls

Call 1

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

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:

115.0ms	(*.f32 alpha alpha)
94.0ms	alpha
93.0ms	(/.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))))
79.0ms	cosTheta

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes57.0ms (0.5%)

Counts

37 → 1

Calls

Call 1

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

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

Calls

3 calls:

33.0ms	cosTheta
11.0ms	(*.f32 alpha alpha)
10.0ms	alpha

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes35.0ms (0.3%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

3 calls:

20.0ms	alpha
7.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
96.8%	1	`cosTheta`
96.8%	1	`alpha`
96.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes21.0ms (0.2%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes20.0ms (0.2%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta
5.0ms	alpha

Results

Accuracy	Segments	Branch
95.4%	1	`cosTheta`
95.4%	1	`alpha`
95.4%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes12.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	cosTheta
3.0ms	(*.f32 alpha alpha)
3.0ms	alpha

Results

Accuracy	Segments	Branch
64.1%	1	`cosTheta`
64.1%	1	`alpha`
64.1%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
64.0%	1	`alpha`
64.0%	1	`(*.f32 alpha alpha)`
64.0%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

Calls

3 calls:

2.0ms	alpha
1.0ms	(*.f32 alpha alpha)
1.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary32`
14×	`+-commutative_binary32`
10×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	115
1	64	115
2	73	115
3	81	115
4	83	115

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.1s (19.4%)

Rules

8558×	`-lowering-.f32`
8558×	`-lowering-.f64`
7162×	`-lowering-.f32`
7162×	`-lowering-.f64`
6516×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	670	10085
1	2295	8225
0	8433	8225
0	224	4532
1	731	3703
2	2928	3619
0	8798	3619
0	21	99
1	158	96
2	1257	96
0	8991	96
0	657	8534
1	2461	6970
0	9103	6970
0	693	8997
1	2518	7405
0	9122	7405
0	13	21
1	44	19
2	160	19
3	684	19
4	2882	19
5	6032	19
0	8041	19

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 323 to 184 computations (43% saved)

preprocess48.0ms (0.4%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 910 to 442 computations (51.4% saved)

analyze87.0ms (0.8%)

sample2.1s (19.4%)

preprocess223.0ms (2%)

explain190.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify195.0ms (1.8%)

localize116.0ms (1.1%)

series103.0ms (0.9%)

rewrite467.0ms (4.3%)

simplify325.0ms (3%)

eval173.0ms (1.6%)

prune223.0ms (2%)

simplify12.0ms (0.1%)

localize271.0ms (2.5%)

series38.0ms (0.3%)

rewrite23.0ms (0.2%)

simplify354.0ms (3.2%)

eval54.0ms (0.5%)

prune59.0ms (0.5%)

simplify11.0ms (0.1%)

localize310.0ms (2.8%)

series128.0ms (1.2%)

rewrite18.0ms (0.2%)

simplify423.0ms (3.9%)

eval67.0ms (0.6%)

prune68.0ms (0.6%)

simplify369.0ms (3.4%)

localize412.0ms (3.8%)

series53.0ms (0.5%)

rewrite430.0ms (3.9%)

simplify432.0ms (4%)

eval147.0ms (1.3%)

prune305.0ms (2.8%)

regimes387.0ms (3.5%)

regimes57.0ms (0.5%)

regimes35.0ms (0.3%)

regimes21.0ms (0.2%)

regimes20.0ms (0.2%)

regimes12.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

simplify10.0ms (0.1%)

soundness2.1s (19.4%)

preprocess48.0ms (0.4%)

end0.0ms (0%)

Profiling