Metrics for GTR1 distribution

analyze105.0ms (0.7%)

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: 69.0ms

ival-<=: 28.0ms (40.5% of total)

ival-mult: 14.0ms (20.2% of total)

...c/correct-round.rkt:119:19: 8.0ms (11.6% of total)

ival-log: 6.0ms (8.7% of total)

ival-div: 3.0ms (4.3% of total)

ival-add: 3.0ms (4.3% of total)

ival-sub: 3.0ms (4.3% of total)

ival-pi: 2.0ms (2.9% of total)

ival-and: 2.0ms (2.9% of total)

const: 1.0ms (1.4% of total)

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

sample1.7s (11.3%)

Results

1.3s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 981.0ms

ival-mult: 305.0ms (31.1% of total)

...c/correct-round.rkt:119:19: 179.0ms (18.3% of total)

ival-log: 118.0ms (12% of total)

ival-<=: 114.0ms (11.6% of total)

ival-div: 79.0ms (8.1% of total)

ival-add: 52.0ms (5.3% of total)

ival-sub: 43.0ms (4.4% of total)

ival-pi: 38.0ms (3.9% of total)

ival-and: 38.0ms (3.9% of total)

const: 11.0ms (1.1% of total)

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

Bogosity

preprocess216.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
1494×	`fnmsub-define`
1320×	`fnmadd-define`
1072×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	128
1	166	116
2	551	114
3	2482	114
0	13	21
1	41	19
2	131	19
3	486	19
4	1421	19
5	3292	19
6	6461	19
0	8135	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 alpha alpha) #s(literal -1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))

Call 2

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

Outputs
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
(/ (+ (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))))
(/ (+ (square cosTheta) -1) (* (log (square cosTheta)) (fma (square alpha) (* (PI) (+ (square cosTheta) -1)) (PI))))

Symmetry

(abs cosTheta)

(abs alpha)

explain149.0ms (1%)

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

88.0ms

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: 16.0ms (43.5% of total)

ival-log: 8.0ms (21.7% of total)

ival-div: 4.0ms (10.9% of total)

ival-sub: 3.0ms (8.1% of total)

ival-add: 3.0ms (8.1% of total)

ival-pi: 2.0ms (5.4% 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 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 alpha alpha) #s(literal 1 binary32)) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Compiler

Compiled 26 to 13 computations (50% saved)

simplify173.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
1494×	`fnmsub-define`
1320×	`fnmadd-define`
1072×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	79
1	41	72
2	131	72
3	486	72
4	1421	71
5	3292	71
6	6461	71
0	8135	71

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize66.0ms (0.5%)

Localize:

Found 4 expressions of interest:

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

Results

49.0ms

256×

valid

Compiler

Compiled 94 to 14 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 8.0ms (45.2% of total)

ival-log: 3.0ms (16.9% of total)

ival-div: 2.0ms (11.3% of total)

ival-pi: 1.0ms (5.6% of total)

ival-sub: 1.0ms (5.6% of total)

ival-add: 1.0ms (5.6% of total)

const: 0.0ms (0% of total)

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

series90.0ms (0.6%)

Counts

7 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
34.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
21.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
8.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
8.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite288.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

2984×	`-lowering-.f32`
2984×	`-lowering-.f64`
1368×	`fma-lowering-fma.f32`
1368×	`fma-lowering-fma.f64`
1146×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	69	57
2	342	57
3	2951	57
0	8218	57

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 431

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))))))
(exp.f32 (.f32 (log.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))) #s(literal -1 binary32)))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))) #s(literal -1 binary32)))
(+.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
(+.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))) #s(literal -1 binary32)) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
(+.f32 (.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)))
(pow.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))) #s(literal 1 binary32))
(pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (pow.f32 (.f32 (.f32 (PI.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)))) #s(literal 2 binary32)) (-.f32 (.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 (PI.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)))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) #s(literal -1 binary32))
(pow.f32 (exp.f32 (log.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))))) #s(literal -1 binary32))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.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 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))))
(fma.f32 alpha (/.f32 alpha (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))) #s(literal -1 binary32)))
(fma.f32 (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))))
(fma.f32 (.f32 alpha alpha) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))) #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))))
(fma.f32 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))))
(fma.f32 #s(literal 1 binary32) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))) #s(literal -1 binary32)))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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))))))
(fma.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))))
(fma.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) #s(literal 1 binary32) (+.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.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))))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))))
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(.f32 #s(literal 2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
(.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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))))) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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))))) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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))))) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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))))) #s(literal 1 binary32)))
(.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)))) (PI.f32))
(.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 (PI.f32) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))))
(.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
(.f32 (neg.f32 (PI.f32)) (neg.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
(.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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))))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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))))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) #s(literal 1 binary32)))
(.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
(.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(.f32 (.f32 #s(literal 1 binary32) (.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))))) (PI.f32))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(.f32 (.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)))) #s(literal 1 binary32)) (PI.f32))
(.f32 (neg.f32 (-.f32 #s(literal 0 binary32) (.f32 (PI.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 (neg.f32 (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
(.f32 (neg.f32 (neg.f32 (PI.f32))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (.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)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) #s(literal 2 binary32)) (log.f32 alpha))
(+.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (PI.f32) (log.f32 alpha) (*.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (PI.f32) (.f32 #s(literal 1 binary32) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (log.f32 alpha) (PI.f32) (*.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal 1 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (.f32 (log.f32 alpha) #s(literal 1 binary32)) (PI.f32) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
(fma.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (PI.f32) (log.f32 alpha)))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
(.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))
(.f32 (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) #s(literal 1 binary32))
(*.f32 (log.f32 alpha) (+.f32 (PI.f32) (PI.f32)))
(.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))
(.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(.f32 (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 (*.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(.f32 (.f32 #s(literal 1 binary32) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/9 binary32))) (pow.f32 (PI.f32) #s(literal 1/9 binary32)))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(.f32 (.f32 (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(+.f32 (.f32 (.f32 alpha alpha) cosTheta) (neg.f32 cosTheta))
(+.f32 (neg.f32 cosTheta) (.f32 (.f32 alpha alpha) cosTheta))
(fma.f32 alpha (*.f32 alpha cosTheta) (neg.f32 cosTheta))
(fma.f32 (*.f32 alpha alpha) cosTheta (neg.f32 cosTheta))
(fma.f32 cosTheta (*.f32 alpha alpha) (neg.f32 cosTheta))
(fma.f32 cosTheta #s(literal -1 binary32) (.f32 (.f32 alpha alpha) cosTheta))
(fma.f32 #s(literal -1 binary32) cosTheta (.f32 (.f32 alpha alpha) cosTheta))
(fma.f32 (*.f32 cosTheta alpha) alpha (neg.f32 cosTheta))
(-.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) cosTheta)
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(+.f32 (.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta)) (.f32 cosTheta (neg.f32 cosTheta)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(+.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)) (.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha)))
(+.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (.f32 (neg.f32 cosTheta) cosTheta))
(+.f32 (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 alpha alpha) (*.f32 cosTheta cosTheta)))
(fma.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
(fma.f32 cosTheta (.f32 (.f32 alpha alpha) cosTheta) (*.f32 cosTheta (neg.f32 cosTheta)))
(fma.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta) (.f32 (.f32 alpha alpha) (.f32 cosTheta cosTheta)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32)))
(fma.f32 (.f32 cosTheta cosTheta) #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)))
(fma.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta (*.f32 (neg.f32 cosTheta) cosTheta))
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta))
(.f32 (.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) cosTheta) cosTheta)
(.f32 (.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))

simplify533.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

5794×	`-lowering-.f32`
5794×	`-lowering-.f64`
2526×	`/-lowering-/.f32`
2526×	`/-lowering-/.f64`
2246×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	2627
1	710	2143
2	2880	2102
0	8581	2102

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval59.0ms (0.4%)

Compiler: Compiled 21912 to 1489 computations (93.2% saved)

prune94.0ms (0.6%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	599	29	628
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	599	30	629

Accuracy

100.0%

Counts

629 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
▶	97.6%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
	98.4%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
▶	98.3%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	95.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
	98.3%	(/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.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 alpha) #s(literal -1 binary32))))
	68.1%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	98.3%	(/.f32 (-.f32 (.f32 (/.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))) (pow.f32 (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))) #s(literal 2 binary32)))
	98.3%	(/.f32 (-.f32 (.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.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))))))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (.f32 (/.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) alpha) (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.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))))
	45.9%	(/.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))))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.4%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	98.3%	(/.f32 #s(literal -1 binary32) (/.f32 (.f32 (.f32 (PI.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 #s(literal 1 binary32) (*.f32 alpha alpha))))
	68.1%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.4%	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
	97.8%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (.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)))))))
	98.1%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (/.f32 #s(literal 1 binary32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	97.7%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))
	97.9%	(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) (/.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 alpha) #s(literal -1 binary32)))))
	97.4%	(exp.f32 (.f32 (log.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))))) #s(literal -1 binary32)))

Compiler

Compiled 1776 to 1001 computations (43.6% saved)

simplify231.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	cost-diff	0	(/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
✓	cost-diff	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	cost-diff	6528	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))))
✓	cost-diff	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 (log.f32 alpha) #s(literal 2 binary32)))
✓	cost-diff	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	cost-diff	0	(.f32 (PI.f32) (.f32 cosTheta cosTheta))
✓	cost-diff	0	(log.f32 alpha)
✓	cost-diff	0	(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
✓	cost-diff	0	(*.f32 alpha alpha)
✓	cost-diff	0	(/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	cost-diff	3712	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))

Rules

3746×	`-lowering-.f32`
3746×	`-lowering-.f64`
1760×	`/-lowering-/.f32`
1760×	`/-lowering-/.f64`
1652×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	439
1	113	422
2	387	420
3	1821	420
4	6774	420
0	8167	420

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize365.0ms (2.5%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
✓	accuracy	99.0%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	accuracy	98.7%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	98.7%	(.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	99.2%	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))
✓	accuracy	98.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))))
✓	accuracy	98.8%	(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	99.9%	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	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)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	98.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.4%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
✓	accuracy	99.2%	(.f32 (PI.f32) (.f32 cosTheta cosTheta))
✓	accuracy	99.2%	(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
✓	accuracy	99.1%	(/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.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)))))
✓	accuracy	99.0%	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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 #s(literal 1 binary32) (.f32 (.f32 (PI.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))))))
✓	accuracy	98.8%	(.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	98.8%	(/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.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)))))

Results

257.0ms

256×

valid

Compiler

Compiled 547 to 34 computations (93.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-div: 17.0ms (34% of total)

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

ival-pow: 7.0ms (14% of total)

ival-log: 4.0ms (8% of total)

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

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

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

const: 1.0ms (2% of total)

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

series164.0ms (1.1%)

Counts

21 → 384

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
54.0ms	cosTheta	@	inf	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))
21.0ms	alpha	@	-inf	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))
13.0ms	cosTheta	@	0	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))
9.0ms	alpha	@	inf	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))
7.0ms	alpha	@	0	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))

rewrite605.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4098×	`-lowering-.f32`
4098×	`-lowering-.f64`
3334×	`/-lowering-/.f32`
3334×	`/-lowering-/.f64`
1308×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	234
1	203	224
2	1473	224
0	8912	224

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 2303

Calls

Call 1

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

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

simplify523.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

8088×	`-lowering-.f32`
8088×	`-lowering-.f64`
3214×	`+-lowering-+.f64`
3214×	`+-lowering-+.f32`
1666×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	730	12357
1	2655	10391
0	9065	10391

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

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

eval678.0ms (4.6%)

Compiler: Compiled 163879 to 5445 computations (96.7% saved)

prune387.0ms (2.7%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	3709	27	3736
Fresh	16	8	24
Picked	5	0	5
Done	0	1	1
Total	3730	36	3766

Accuracy

100.0%

Counts

3766 → 36

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 (PI.f32) cosTheta)) cosTheta)
▶	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (PI.f32)) (neg.f32 (*.f32 cosTheta cosTheta)))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.7%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
	95.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.3%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (log.f32 alpha) #s(literal 1/2 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
▶	97.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	68.1%	(/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	68.1%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
▶	98.4%	(/.f32 (-.f32 (/.f32 (/.f32 (.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.4%	(/.f32 (-.f32 (.f32 (/.f32 alpha (.f32 (log.f32 alpha) (.f32 #s(literal 2 binary32) (PI.f32)))) alpha) (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
	95.3%	(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (log.f32 alpha))))
	97.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (.f32 (/.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) alpha) (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
▶	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.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))))
	45.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (+.f32 (.f32 (log.f32 alpha) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (/.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.2%	(/.f32 (.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
	98.3%	(/.f32 (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) #s(literal 2 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (log.f32 alpha) (*.f32 (PI.f32) cosTheta)) cosTheta))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)) (PI.f32)))
▶	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta)))
	98.3%	(/.f32 #s(literal -1 binary32) (/.f32 (.f32 (.f32 (PI.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 #s(literal 1 binary32) (*.f32 alpha alpha))))
	98.2%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (PI.f32)))

Compiler

Compiled 1454 to 965 computations (33.6% saved)

simplify227.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(*.f32 (PI.f32) (log.f32 alpha))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
✓	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 alpha)
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta))
✓	cost-diff	0	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) cosTheta) cosTheta)
✓	cost-diff	0	(log.f32 alpha)
✓	cost-diff	0	(.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta)))
✓	cost-diff	0	(/.f32 (*.f32 alpha alpha) (log.f32 alpha))
✓	cost-diff	0	(/.f32 (/.f32 (*.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32))
✓	cost-diff	0	(/.f32 (-.f32 (/.f32 (/.f32 (.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
✓	cost-diff	3264	(-.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))

Rules

3550×	`-lowering-.f32`
3550×	`-lowering-.f64`
2268×	`/-lowering-/.f32`
2268×	`/-lowering-/.f64`
1534×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	289
1	101	283
2	292	283
3	1056	277
4	3444	268
0	8125	268

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize259.0ms (1.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.2%	(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
✓	accuracy	99.0%	(/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
✓	accuracy	98.8%	(*.f32 (PI.f32) (log.f32 alpha))
✓	accuracy	98.7%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
✓	accuracy	99.9%	(.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
✓	accuracy	99.9%	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
✓	accuracy	98.9%	(/.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	98.8%	(.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.2%	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta))
✓	accuracy	99.1%	(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
✓	accuracy	99.1%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
✓	accuracy	99.5%	(.f32 (.f32 (PI.f32) cosTheta) cosTheta)
✓	accuracy	99.4%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta)))
✓	accuracy	99.2%	(.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta))
✓	accuracy	99.0%	(*.f32 (PI.f32) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
✓	accuracy	99.1%	(-.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))
✓	accuracy	98.9%	(/.f32 (*.f32 alpha alpha) (log.f32 alpha))
✓	accuracy	98.9%	(/.f32 (-.f32 (/.f32 (/.f32 (.f32 alpha alpha) (log.f32 alpha)) #s(literal 2 binary32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))

Results

195.0ms

256×

valid

Compiler

Compiled 331 to 36 computations (89.1% saved)

Precisions

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

ival-div: 22.0ms (39.7% of total)

ival-mult: 22.0ms (39.7% of total)

ival-sub: 4.0ms (7.2% of total)

ival-log: 4.0ms (7.2% of total)

ival-add: 2.0ms (3.6% of total)

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

const: 1.0ms (1.8% of total)

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

series39.0ms (0.3%)

Counts

22 → 372

Calls

Call 1

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

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

Calls

93 calls:

Time	Variable		Point	Expression
8.0ms	alpha	@	0	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
1.0ms	alpha	@	-inf	(/ (- (/ (/ (* alpha alpha) (log alpha)) 2) (/ 1/2 (log alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
1.0ms	alpha	@	inf	(/ (- (* alpha alpha) 1) (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)))
1.0ms	cosTheta	@	inf	(/ (- (/ (/ (* alpha alpha) (log alpha)) 2) (/ 1/2 (log alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite530.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4438×	`-lowering-.f32`
4438×	`-lowering-.f64`
4332×	`/-lowering-/.f32`
4332×	`/-lowering-/.f64`
966×	`frac-2neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	182
1	195	176
2	1403	170
0	8727	170

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1613

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (log.f32 alpha) #s(literal -1/2 binary32))))
(+.f32 (/.f32 (*.f32 alpha alpha) (/.f32 (log.f32 alpha) #s(literal 1/2 binary32))) (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)))
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(*.f32 (log.f32 alpha) (PI.f32))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 binary32) (.f32 (log.f32 alpha) (PI.f32))))
(.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 1 binary32))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (log.f32 alpha)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (log.f32 alpha)))
(*.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (neg.f32 (PI.f32)) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))
(.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 (log.f32 alpha) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(PI.f32)
(log1p.f32 (expm1.f32 (PI.f32)))
(neg.f32 (neg.f32 (PI.f32)))
(exp.f32 (log.f32 (PI.f32)))
(exp.f32 (.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))) #s(literal 3 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1/3 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32))) #s(literal 2 binary32)))
(+.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal -1 binary32))
(fabs.f32 (PI.f32))
(pow.f32 (PI.f32) #s(literal 1 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 3 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/2 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 1/3 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 2 binary32))
(pow.f32 (E.f32) (log.f32 (PI.f32)))
(-.f32 #s(literal 0 binary32) (neg.f32 (PI.f32)))
(-.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32))
(-.f32 (/.f32 (+.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32)) #s(literal 1 binary32))
(/.f32 (PI.f32) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (neg.f32 (PI.f32)) #s(literal -1 binary32))
(sqrt.f32 (*.f32 (PI.f32) (PI.f32)))
(cbrt.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))
(*.f32 (PI.f32) #s(literal 1 binary32))
(*.f32 (PI.f32) (log.f32 (E.f32)))
(*.f32 #s(literal 1 binary32) (PI.f32))
(*.f32 #s(literal -1 binary32) (neg.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (log.f32 (exp.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)))))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32))))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) #s(literal 2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (neg.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (log.f32 (exp.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (neg.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))))
(*.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))))
(*.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/3 binary32))))
(*.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32))))
(*.f32 (pow.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal 1/3 binary32)) #s(literal 3 binary32)) (pow.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 1/3 binary32)) #s(literal 3 binary32)))
(*.f32 (pow.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32)) #s(literal 3 binary32)) (pow.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32)) #s(literal 3 binary32)))
(.f32 (pow.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 1/3 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32)) #s(literal 1/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32)))
(.f32 (exp.f32 (.f32 #s(literal 2 binary32) (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32))))) (exp.f32 (.f32 #s(literal 1/3 binary32) (log.f32 (PI.f32)))))
(.f32 (exp.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32)))) (exp.f32 (*.f32 #s(literal 1/2 binary32) (log.f32 (PI.f32)))))
(.f32 (cbrt.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) #s(literal 1/3 binary32)))
(*.f32 (cbrt.f32 (pow.f32 (PI.f32) #s(literal 5/2 binary32))) (pow.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) #s(literal 1/3 binary32)))
(*.f32 (sqrt.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(.f32 (sqrt.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(*.f32 (neg.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(*.f32 (neg.f32 (-.f32 #s(literal 0 binary32) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(log.f32 (exp.f32 (PI.f32)))
(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (exp.f32 (PI.f32)))))
(expm1.f32 (log1p.f32 (PI.f32)))
(*.f32 (PI.f32) cosTheta)
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) cosTheta))
(*.f32 cosTheta (PI.f32))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/3 binary32)) cosTheta))
(.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/2 binary32)) cosTheta))
(.f32 (.f32 cosTheta (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/3 binary32)))
(.f32 (.f32 cosTheta (pow.f32 (PI.f32) #s(literal 1/2 binary32))) (pow.f32 (PI.f32) #s(literal 1/2 binary32)))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))
(+.f32 (.f32 (log.f32 alpha) (-.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))))
(fma.f32 #s(literal 1 binary32) (log.f32 alpha) (.f32 (log.f32 alpha) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta))))
(.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32))
(neg.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))))
(neg.f32 (/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) #s(literal 1 binary32)))
(exp.f32 (.f32 (log.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))) #s(literal -1 binary32)))
(+.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))
(+.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #s(literal 1 binary32)) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(+.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (.f32 (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) #s(literal 1 binary32)))
(+.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)) (/.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))))
(pow.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #s(literal 1 binary32))
(pow.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))))
(-.f32 (/.f32 #s(literal 0 binary32) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
(/.f32 #s(literal -1 binary32) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))))))
(/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) #s(literal 1 binary32))
(/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))
(/.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) #s(literal -1 binary32))
(/.f32 (.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)))
(.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
(.f32 #s(literal -1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
(.f32 (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))) #s(literal 1 binary32))
(.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))
(.f32 (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
(.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha))))

simplify431.0ms (3%)

Algorithm

1×	egg-herbie

Rules

4978×	`-lowering-.f32`
4978×	`-lowering-.f64`
2756×	`/-lowering-/.f32`
2756×	`/-lowering-/.f64`
1730×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	445	6833
1	1570	5772
2	6647	5756
0	8023	5756

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

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

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

eval457.0ms (3.1%)

Compiler: Compiled 74917 to 5116 computations (93.2% saved)

prune522.0ms (3.6%)

Pruning

39 alts after pruning (35 fresh and 4 done)

	Pruned	Kept	Total
New	2501	22	2523
Fresh	17	13	30
Picked	2	3	5
Done	0	1	1
Total	2520	39	2559

Accuracy

100.0%

Counts

2559 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(/.f32 (fma.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))))
	1.8%	(/.f32 (/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) cosTheta) (neg.f32 cosTheta)) (PI.f32))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 cosTheta (log.f32 alpha))) cosTheta) (PI.f32))
✓	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (*.f32 cosTheta (log.f32 alpha))) cosTheta)
	1.8%	(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (PI.f32)) (neg.f32 (*.f32 cosTheta cosTheta)))
	98.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	97.7%	(/.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 1/2 binary32))))
	95.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	98.3%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (log.f32 alpha) #s(literal 1/2 binary32)) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
▶	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta))) cosTheta)
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))) (PI.f32))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
✓	97.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	95.0%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
	83.2%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))
	97.7%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))))
▶	68.0%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta (log.f32 alpha))) (.f32 (PI.f32) cosTheta))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 alpha)))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	97.6%	(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (/.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
	68.1%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	95.3%	(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (log.f32 alpha))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (.f32 (/.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) alpha) (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) #s(literal 2 binary32))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 alpha) (*.f32 (PI.f32) #s(literal 2 binary32))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.7%	(/.f32 (.f32 (.f32 alpha 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))))
	97.5%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (log.f32 alpha) (/.f32 #s(literal 1/2 binary32) (PI.f32)))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	97.6%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))) (/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha))))
▶	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta))
✓	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (*.f32 (PI.f32) cosTheta) cosTheta)))
	68.0%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))))
	97.6%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (PI.f32) #s(literal 1/2 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))

Compiler

Compiled 1308 to 925 computations (29.3% saved)

simplify256.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	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)) (log.f32 alpha))
✓	cost-diff	0	(/.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 1/2 binary32))))
✓	cost-diff	0	(PI.f32)
✓	cost-diff	0	(*.f32 (PI.f32) (log.f32 alpha))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
✓	cost-diff	0	(log.f32 alpha)
✓	cost-diff	0	(.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta))
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta)))
✓	cost-diff	0	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta))) cosTheta)
✓	cost-diff	0	(*.f32 (PI.f32) (log.f32 alpha))
✓	cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 alpha)) cosTheta)
✓	cost-diff	0	(.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta)
✓	cost-diff	0	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta))
✓	cost-diff	0	(*.f32 alpha alpha)
✓	cost-diff	0	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	cost-diff	0	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	cost-diff	192	(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))

Rules

2956×	`-lowering-.f32`
2956×	`-lowering-.f64`
1956×	`+-lowering-+.f64`
1956×	`+-lowering-+.f32`
1910×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	268
1	109	265
2	316	265
3	1284	240
4	3381	238
5	5983	238
0	8304	238

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize346.0ms (2.4%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32)))
✓	accuracy	99.9%	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	accuracy	99.0%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha))
✓	accuracy	98.9%	(/.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 1/2 binary32))))
✓	accuracy	100.0%	(+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta))
✓	accuracy	99.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
✓	accuracy	99.0%	(/.f32 #s(literal 1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
✓	accuracy	98.8%	(*.f32 (PI.f32) (log.f32 alpha))
✓	accuracy	99.6%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta))) cosTheta)
✓	accuracy	99.1%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta)))
✓	accuracy	99.0%	(*.f32 (PI.f32) cosTheta)
✓	accuracy	98.8%	(.f32 (log.f32 alpha) (.f32 (PI.f32) cosTheta))
✓	accuracy	99.5%	(.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta)
✓	accuracy	99.4%	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (*.f32 (PI.f32) (log.f32 alpha)) cosTheta) cosTheta))
✓	accuracy	99.2%	(.f32 (.f32 (PI.f32) (log.f32 alpha)) cosTheta)
✓	accuracy	98.8%	(*.f32 (PI.f32) (log.f32 alpha))
✓	accuracy	99.3%	(/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))
✓	accuracy	99.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	accuracy	98.9%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	98.5%	(.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (*.f32 alpha alpha))))

Results

264.0ms

256×

valid

Compiler

Compiled 294 to 37 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 30.0ms (49.4% of total)

ival-div: 18.0ms (29.6% of total)

ival-add: 5.0ms (8.2% of total)

ival-log: 4.0ms (6.6% of total)

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

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

const: 1.0ms (1.6% of total)

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

series47.0ms (0.3%)

Counts

22 → 360

Calls

Call 1

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

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

Calls

90 calls:

Time	Variable		Point	Expression
26.0ms	cosTheta	@	0	(* (* (PI) (log alpha)) cosTheta)
1.0ms	cosTheta	@	0	(/ (/ (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha)))) (* (log alpha) 2)) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	cosTheta	@	inf	(/ (/ (* (* alpha alpha) (+ 1 (/ -1 (* alpha alpha)))) (* (log alpha) 2)) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	alpha	@	-inf	(/ (/ 1/2 (* (PI) (log alpha))) (+ -1 (* cosTheta cosTheta)))
1.0ms	alpha	@	inf	(/ (/ 1/2 (* (PI) (log alpha))) (+ -1 (* cosTheta cosTheta)))

rewrite362.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4516×	`/-lowering-/.f32`
4516×	`/-lowering-/.f64`
4430×	`-lowering-.f32`
4430×	`-lowering-.f64`
1420×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	171
1	202	170
2	1382	150
0	8531	150

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1188

Calls

Call 1

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

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

simplify701.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

6572×	`-lowering-.f32`
6572×	`-lowering-.f64`
3236×	`/-lowering-/.f32`
3236×	`/-lowering-/.f64`
2580×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	5368
1	1156	4637
2	4861	4606
0	9286	4606

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

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

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

eval283.0ms (1.9%)

Compiler: Compiled 41337 to 4063 computations (90.2% saved)

prune323.0ms (2.2%)

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	1984	21	2005
Fresh	22	8	30
Picked	4	1	5
Done	2	2	4
Total	2012	32	2044

Accuracy

100.0%

Counts

2044 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.0%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (log.f32 alpha)) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
	97.4%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (/.f32 (log.f32 alpha) (.f32 alpha alpha))) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	97.7%	(/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) #s(literal -1 binary32)) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	97.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (.f32 (PI.f32) (log.f32 (E.f32))) #s(literal 1/2 binary32))))
	95.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 alpha)) (.f32 #s(literal 2 binary32) (PI.f32)))
	95.6%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.4%	(/.f32 (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 alpha alpha)) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	68.0%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (log.f32 alpha) (/.f32 #s(literal 1/2 binary32) (PI.f32)))) (+.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))
	97.4%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (log.f32 alpha) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
✓	97.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	95.0%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
	83.2%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (*.f32 alpha alpha)))
	97.7%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (.f32 cosTheta cosTheta) (/.f32 #s(literal 1 binary32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))))
✓	68.0%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
	68.0%	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))
	97.6%	(/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (/.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	95.3%	(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (log.f32 alpha))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (-.f32 (.f32 (/.f32 (-.f32 #s(literal 0 binary32) (log.f32 alpha)) alpha) (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (.f32 cosTheta cosTheta))))))
✓	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.3%	(/.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))) (.f32 alpha alpha)) (/.f32 (log.f32 alpha) #s(literal 1/2 binary32)))
	97.5%	(/.f32 (.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (PI.f32) #s(literal 1/2 binary32))) (/.f32 #s(literal 1 binary32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
	68.0%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))) (PI.f32))
	97.5%	(/.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 alpha (/.f32 alpha (log.f32 alpha)))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	95.5%	(/.f32 (.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (*.f32 (PI.f32) (log.f32 alpha)))
	97.6%	(/.f32 (.f32 (.f32 alpha alpha) (/.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (log.f32 alpha))) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	97.4%	(/.f32 (.f32 alpha (/.f32 (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha))) (log.f32 alpha))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (PI.f32) #s(literal 1/2 binary32))))
	97.7%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (PI.f32) #s(literal 1/2 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.6%	(/.f32 #s(literal 1/2 binary32) (.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) (log.f32 alpha))) (PI.f32)))
	66.7%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	98.1%	(.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) (.f32 (.f32 alpha alpha) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))))))
	98.0%	(.f32 alpha (/.f32 (.f32 alpha (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha))) (.f32 (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))) (/.f32 (log.f32 alpha) (/.f32 #s(literal 1/2 binary32) (PI.f32))))))

Compiler

Compiled 2756 to 807 computations (70.7% saved)

regimes171.0ms (1.2%)

Counts

100 → 1

Calls

Call 1

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

Calls

4 calls:

56.0ms	(/.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))))
46.0ms	cosTheta
31.0ms	(*.f32 alpha alpha)
28.0ms	alpha

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes57.0ms (0.4%)

Counts

61 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

18.0ms	(*.f32 alpha alpha)
17.0ms	alpha
16.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta`
98.3%	1	`alpha`
98.3%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes56.0ms (0.4%)

Counts

59 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

18.0ms	alpha
17.0ms	cosTheta
16.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta`
98.2%	1	`alpha`
98.2%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes53.0ms (0.4%)

Counts

54 → 1

Calls

Call 1

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

16.0ms	(*.f32 alpha alpha)
16.0ms	alpha
13.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes48.0ms (0.3%)

Counts

38 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.6%	1	`cosTheta`
97.6%	1	`alpha`
97.6%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes34.0ms (0.2%)

Counts

36 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(*.f32 alpha alpha)
9.0ms	alpha
9.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes27.0ms (0.2%)

Counts

27 → 1

Calls

Call 1

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

10.0ms	alpha
7.0ms	cosTheta
7.0ms	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes13.0ms (0.1%)

Accuracy

Total -20.8b remaining (-194.6%)

Threshold costs -20.8b (-194.6%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	cosTheta
6.0ms	alpha

Results

Accuracy	Segments	Branch
66.7%	1	`cosTheta`
66.7%	1	`alpha`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary32`
24×	`+-commutative_binary32`
16×	`sub-neg_binary32`
10×	`neg-sub0_binary32`
10×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	138
1	83	138
2	98	138
3	114	138
4	118	138

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

soundness2.9s (19.6%)

Rules

6572×	`-lowering-.f32`
6572×	`-lowering-.f64`
5794×	`-lowering-.f32`
5794×	`-lowering-.f64`
4978×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	213	2627
1	710	2143
2	2880	2102
0	8581	2102
0	340	5368
1	1156	4637
2	4861	4606
0	9286	4606
0	35	182
1	195	176
2	1403	170
0	8727	170
0	13	62
1	69	57
2	342	57
3	2951	57
0	8218	57
0	33	234
1	203	224
2	1473	224
0	8912	224
0	445	6833
1	1570	5772
2	6647	5756
0	8023	5756
0	36	171
1	202	170
2	1382	150
0	8531	150

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
1×	iter limit
1×	node limit

Compiler

Compiled 284 to 150 computations (47.2% saved)

preprocess97.0ms (0.7%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 956 to 456 computations (52.3% saved)

analyze105.0ms (0.7%)

sample1.7s (11.3%)

preprocess216.0ms (1.5%)

explain149.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify173.0ms (1.2%)

localize66.0ms (0.5%)

series90.0ms (0.6%)

rewrite288.0ms (2%)

simplify533.0ms (3.7%)

eval59.0ms (0.4%)

prune94.0ms (0.6%)

simplify231.0ms (1.6%)

localize365.0ms (2.5%)

series164.0ms (1.1%)

rewrite605.0ms (4.1%)

simplify523.0ms (3.6%)

eval678.0ms (4.6%)

prune387.0ms (2.7%)

simplify227.0ms (1.6%)

localize259.0ms (1.8%)

series39.0ms (0.3%)

rewrite530.0ms (3.6%)

simplify431.0ms (3%)

eval457.0ms (3.1%)

prune522.0ms (3.6%)

simplify256.0ms (1.8%)

localize346.0ms (2.4%)

series47.0ms (0.3%)

rewrite362.0ms (2.5%)

simplify701.0ms (4.8%)

eval283.0ms (1.9%)

prune323.0ms (2.2%)

regimes171.0ms (1.2%)

regimes57.0ms (0.4%)

regimes56.0ms (0.4%)

regimes53.0ms (0.4%)

regimes48.0ms (0.3%)

regimes34.0ms (0.2%)

regimes27.0ms (0.2%)

regimes13.0ms (0.1%)

simplify10.0ms (0.1%)

soundness2.9s (19.6%)

preprocess97.0ms (0.7%)

end0.0ms (0%)

Profiling