Metrics for GTR1 distribution

analyze117.0ms (1.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.6%	99.4%	0%	0%	0%	0
0%	0%	0.6%	99.4%	0%	0%	0%	1
0%	0%	0.6%	99.4%	0%	0%	0%	2
0%	0%	0.6%	99.4%	0%	0%	0%	3
0%	0%	0.6%	99.4%	0%	0%	0%	4
50%	0.3%	0.3%	99.4%	0%	0%	0%	5
50%	0.3%	0.3%	99.4%	0%	0%	0%	6
75%	0.5%	0.2%	99.4%	0%	0%	0%	7
75%	0.5%	0.2%	99.4%	0%	0%	0%	8
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	9
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	10
93.7%	0.6%	0%	99.4%	0%	0%	0%	11
93.7%	0.6%	0%	99.4%	0%	0%	0%	12

Compiler

Compiled 41 to 22 computations (46.3% saved)

Precisions

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

ival-<=: 42.0ms (50.2% of total)

ival-mult: 14.0ms (16.7% of total)

...c/correct-round.rkt:119:19: 8.0ms (9.6% of total)

ival-log: 7.0ms (8.4% of total)

ival-div: 3.0ms (3.6% of total)

ival-add: 3.0ms (3.6% of total)

ival-sub: 3.0ms (3.6% of total)

ival-pi: 2.0ms (2.4% of total)

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

const: 1.0ms (1.2% of total)

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

sample1.8s (16.6%)

Results

1.4s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-mult: 330.0ms (31.4% of total)

ival-<=: 186.0ms (17.7% of total)

...c/correct-round.rkt:119:19: 170.0ms (16.2% of total)

ival-log: 124.0ms (11.8% of total)

ival-div: 64.0ms (6.1% of total)

ival-add: 46.0ms (4.4% of total)

ival-sub: 44.0ms (4.2% of total)

ival-pi: 41.0ms (3.9% of total)

ival-and: 26.0ms (2.5% of total)

const: 14.0ms (1.3% of total)

backward-pass: 4.0ms (0.4% of total)

Bogosity

preprocess215.0ms (2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	128
1	175	116
2	686	114
3	3787	114
0	13	21
1	44	19
2	160	19
3	684	19
4	2882	19
5	6032	19
0	8041	19

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

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

Outputs

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

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

Call 2

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

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

Symmetry

(abs cosTheta)

(abs alpha)

explain147.0ms (1.4%)

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: 38.0ms

ival-mult: 17.0ms (45% of total)

ival-log: 7.0ms (18.5% of total)

ival-sub: 4.0ms (10.6% of total)

ival-div: 4.0ms (10.6% of total)

ival-add: 3.0ms (7.9% of total)

ival-pi: 2.0ms (5.3% of total)

const: 1.0ms (2.6% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

98.6%

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

▶

98.6%

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

Compiler

Compiled 52 to 27 computations (48.1% saved)

simplify166.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize104.0ms (1%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.5%	(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
✓	accuracy	99.1%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.5%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.1%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

75.0ms

256×

valid

Compiler

Compiled 181 to 22 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 14.0ms (48.1% of total)

ival-div: 5.0ms (17.2% of total)

ival-log: 4.0ms (13.7% of total)

ival-add: 4.0ms (13.7% of total)

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

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

const: 1.0ms (3.4% of total)

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

series67.0ms (0.6%)

Counts

11 → 192

Calls

Call 1

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

48 calls:

Time	Variable		Point	Expression
24.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
11.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
5.0ms	alpha	@	inf	(/ (+ (* alpha alpha) -1) (PI))
4.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
4.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))

rewrite434.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	92
1	158	89
2	1257	89
0	8991	89

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 945

Calls

Call 1

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

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

simplify353.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	4283
1	731	3519
2	2928	3443
0	8798	3443

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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

eval128.0ms (1.2%)

Compiler: Compiled 62436 to 3604 computations (94.2% saved)

prune187.0ms (1.8%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	1431	26	1457
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	1431	28	1459

Accuracy

99.9%

Counts

1459 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (+.f32 #s(literal 1 binary32) (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
▶	98.5%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 alpha alpha)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.3%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (/.f32 (+.f32 (.f32 (+.f32 alpha #s(literal -1 binary32)) alpha) (.f32 (+.f32 alpha #s(literal -1 binary32)) #s(literal 1 binary32))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
✓	98.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	95.4%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	98.5%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	67.0%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) #s(literal 2 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	45.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (/.f32 (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))) (.f32 alpha alpha)))))
	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 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	97.9%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (/.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 1/2 binary32)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))

Compiler

Compiled 1646 to 869 computations (47.2% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	618

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize394.0ms (3.7%)

Localize:

Found 20 expressions of interest:

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

Results

308.0ms

256×

invalid

Compiler

Compiled 621 to 48 computations (92.3% saved)

Precisions

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

ival-mult: 24.0ms (37% of total)

ival-div: 20.0ms (30.9% of total)

ival-add: 10.0ms (15.4% of total)

ival-sub: 4.0ms (6.2% of total)

ival-log: 4.0ms (6.2% of total)

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

const: 1.0ms (1.5% of total)

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

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

series47.0ms (0.4%)

Counts

26 → 384

Calls

Call 1

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

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

Calls

102 calls:

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

rewrite22.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	347

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify505.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

5666×	`-lowering-.f32`
5666×	`-lowering-.f64`
3850×	`+-lowering-+.f64`
3850×	`+-lowering-+.f32`
1816×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	712	9863
1	2539	7842
0	8849	7842

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

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

eval119.0ms (1.1%)

Compiler: Compiled 29434 to 844 computations (97.1% saved)

prune70.0ms (0.7%)

Pruning

32 alts after pruning (30 fresh and 2 done)

	Pruned	Kept	Total
New	777	14	791
Fresh	5	16	21
Picked	5	0	5
Done	0	2	2
Total	787	32	819

Accuracy

100.0%

Counts

819 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 alpha alpha)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
▶	-0.0%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	97.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
✓	98.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	95.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	97.8%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	83.3%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	83.3%	(/.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	1.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))
	67.0%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	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))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (/.f32 (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))) (.f32 alpha alpha)))))
	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 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.1%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	95.0%	(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	67.0%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
▶	96.6%	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	97.4%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))

Compiler

Compiled 1682 to 947 computations (43.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

40×	`-lowering-.f32`
40×	`-lowering-.f64`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
14×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	497

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize312.0ms (2.9%)

Localize:

Found 20 expressions of interest:

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

Results

189.0ms

256×

invalid

Compiler

Compiled 500 to 52 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-mult: 34.0ms (43.1% of total)

ival-div: 23.0ms (29.1% of total)

ival-add: 8.0ms (10.1% of total)

ival-log: 7.0ms (8.9% of total)

ival-sub: 5.0ms (6.3% of total)

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

const: 1.0ms (1.3% of total)

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

series107.0ms (1%)

Counts

26 → 336

Calls

Call 1

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

Outputs
#<alt (/ -1/2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))>
#<alt (- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (pow (- 1 (pow cosTheta 2)) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))>
#<alt (/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))>
#<alt (- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (- 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 (pow cosTheta 2)) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (- 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 (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 (pow cosTheta 2)) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (- 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 (pow cosTheta 2)) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (- 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) (* -1 (log (/ -1 alpha)))))))>
#<alt (+ (* -1 (/ (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ (- 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)))))))))>
#<alt (- (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (- 1 (pow cosTheta 2))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))>
#<alt (- (+ (* -1 (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 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 (- 1 (pow cosTheta 2)) 2)) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* -1 (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (- 1 (pow cosTheta 2))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 2) (* (pow cosTheta 4) (* (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 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))>
#<alt (+ (* -1/4 (/ (* (pow alpha 2) (* (pow cosTheta 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1)))) (* (pow (PI) 2) (pow (log alpha) 2)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (* 1/8 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2) (- (pow alpha 2) 1)))) (* (pow (PI) 3) (pow (log alpha) 3)))) (* 1/4 (/ (* (pow alpha 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1))) (* (pow (PI) 2) (pow (log alpha) 2)))))))>
#<alt (+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1/16 (/ (* (pow alpha 6) (* (pow cosTheta 2) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3) (- (pow alpha 2) 1)))) (* (pow (PI) 4) (pow (log alpha) 4)))) (* -1/8 (/ (* (pow alpha 4) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2) (- (pow alpha 2) 1))) (* (pow (PI) 3) (pow (log alpha) 3)))))) (* 1/4 (/ (* (pow alpha 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1))) (* (pow (PI) 2) (pow (log alpha) 2)))))))>
#<alt (/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (/ (- (+ (* -2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -8 (/ (* (pow (PI) 3) (* (pow (log alpha) 3) (- (pow alpha 2) 1))) (* (pow alpha 8) (* (pow cosTheta 6) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 4))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* -4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))))) (pow cosTheta 2))>
#<alt (/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (/ (- (+ (* -2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* 4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))) (pow cosTheta 2))>
#<alt (/ (- (+ (* -8 (/ (* (pow (PI) 3) (* (pow (log alpha) 3) (- (pow alpha 2) 1))) (* (pow alpha 8) (* (pow cosTheta 6) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 4))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* -4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))))) (pow cosTheta 2))>
#<alt -1>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (- (pow alpha 2) 1)>
#<alt (pow alpha 2)>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
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#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (pow alpha 2)>
#<alt (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))>
#<alt (* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))>
#<alt (* 2 (* (PI) (log alpha)))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))>
#<alt (/ 1 (* (pow cosTheta 2) (PI)))>
#<alt (/ 1 (* (pow cosTheta 2) (PI)))>
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#<alt (/ 1 (pow cosTheta 2))>
#<alt (/ 1 (pow cosTheta 2))>
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#<alt (/ 1 (pow cosTheta 2))>
#<alt (/ 1 (pow cosTheta 2))>
#<alt (pow cosTheta 2)>
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#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
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#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (pow cosTheta 2)>
#<alt (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha))))>
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#<alt (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))>
#<alt (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))>
#<alt (* -1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log (/ 1 alpha)))))>
#<alt (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))>
#<alt (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))>
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#<alt (* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ -1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ -1 alpha))))))))>
#<alt (/ (- (pow alpha 2) 1) (* (PI) (log (pow alpha 2))))>
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#<alt (- (+ (* (pow cosTheta 2) (- (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ 1 (* (PI) (log (pow alpha 2)))))) (/ (pow alpha 2) (* (PI) (log (pow alpha 2))))) (/ 1 (* (PI) (log (pow alpha 2)))))>
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#<alt (* (pow cosTheta 2) (- (+ (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2))))))))>
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#<alt (* (pow cosTheta 2) (- (+ (/ (pow alpha 2) (* (PI) (log (pow alpha 2)))) (/ (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))) (+ (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2))))))))>
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#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>
#<alt (* -1 cosTheta)>

Calls

87 calls:

Time	Variable		Point	Expression
31.0ms	alpha	@	-inf	(log alpha)
9.0ms	alpha	@	-inf	(* (* alpha alpha) (+ (* (* cosTheta cosTheta) (* (PI) (* (log alpha) 2))) (/ (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)) (* alpha alpha))))
7.0ms	alpha	@	inf	(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* -1 cosTheta) cosTheta))))
6.0ms	cosTheta	@	inf	(/ (- (* alpha alpha) 1) (* (* alpha alpha) (+ (* (* cosTheta cosTheta) (* (PI) (* (log alpha) 2))) (/ (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)) (* alpha alpha)))))
6.0ms	alpha	@	inf	(* (* alpha alpha) (+ (* (* cosTheta cosTheta) (* (PI) (* (log alpha) 2))) (/ (* (* (log alpha) (- 1 (* cosTheta cosTheta))) (* (PI) 2)) (* alpha alpha))))

rewrite22.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

40×	`-lowering-.f32`
40×	`-lowering-.f64`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
14×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	263

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify435.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

7072×	`-lowering-.f32`
7072×	`-lowering-.f64`
4058×	`/-lowering-/.f32`
4058×	`/-lowering-/.f64`
1752×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	539	7615
1	1990	6341
0	8251	6341

Stop Event

1×	iter limit
1×	node limit

Counts

336 → 336

Calls

Call 1

Inputs
(/ -1/2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(- (* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* -1 (/ (* (pow alpha 2) (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (- 1 (pow cosTheta 2)))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* (pow alpha 2) (- (/ (* (pow alpha 2) (* (pow cosTheta 4) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2)))))))) (pow (- 1 (pow cosTheta 2)) 2)) (/ (* (pow cosTheta 2) (- (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (- 1 (pow cosTheta 2)))))) (* -1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (pow (- 1 (pow cosTheta 2)) 2))))))) (* 1/2 (/ 1 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (+ (* -1/2 (/ (- 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 (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 (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 (pow cosTheta 2)) 2) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 6) (pow cosTheta 4)))) (+ (* -1/2 (/ (- 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 (pow cosTheta 2)) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (- 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 (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)))))))))
(- (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (- 1 (pow cosTheta 2))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(- (+ (* -1 (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 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 (- 1 (pow cosTheta 2)) 2)) (* (pow alpha 6) (pow cosTheta 4)))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (+ (* -1 (/ (* (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (- 1 (pow cosTheta 2))) (* (pow alpha 4) (pow cosTheta 2)))) (+ (* 1/2 (/ (- 1 (pow cosTheta 2)) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))))))
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(+ (* -1/4 (/ (* (pow alpha 2) (* (pow cosTheta 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1)))) (* (pow (PI) 2) (pow (log alpha) 2)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (* 1/8 (/ (* (pow alpha 4) (* (pow cosTheta 2) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2) (- (pow alpha 2) 1)))) (* (pow (PI) 3) (pow (log alpha) 3)))) (* 1/4 (/ (* (pow alpha 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1))) (* (pow (PI) 2) (pow (log alpha) 2)))))))
(+ (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))) (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1/16 (/ (* (pow alpha 6) (* (pow cosTheta 2) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3) (- (pow alpha 2) 1)))) (* (pow (PI) 4) (pow (log alpha) 4)))) (* -1/8 (/ (* (pow alpha 4) (* (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2) (- (pow alpha 2) 1))) (* (pow (PI) 3) (pow (log alpha) 3)))))) (* 1/4 (/ (* (pow alpha 2) (* (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) (- (pow alpha 2) 1))) (* (pow (PI) 2) (pow (log alpha) 2)))))))
(/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(/ (- (+ (* -2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))) (pow cosTheta 2))
(/ (- (+ (* 4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))) (pow cosTheta 2))
(/ (- (+ (* -8 (/ (* (pow (PI) 3) (* (pow (log alpha) 3) (- (pow alpha 2) 1))) (* (pow alpha 8) (* (pow cosTheta 6) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 4))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* -4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))))) (pow cosTheta 2))
(/ (- (pow alpha 2) 1) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(/ (- (+ (* -2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))) (pow cosTheta 2))
(/ (- (+ (* 4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))) (pow cosTheta 2))
(/ (- (+ (* -8 (/ (* (pow (PI) 3) (* (pow (log alpha) 3) (- (pow alpha 2) 1))) (* (pow alpha 8) (* (pow cosTheta 6) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 4))))) (/ 1 (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))) (+ (* -4 (/ (* (pow (PI) 2) (* (pow (log alpha) 2) (- (pow alpha 2) 1))) (* (pow alpha 6) (* (pow cosTheta 4) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 3))))) (+ (* 2 (/ (* (PI) (* (log alpha) (- (pow alpha 2) 1))) (* (pow alpha 4) (* (pow cosTheta 2) (pow (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))) 2))))) (/ 1 (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))))) (pow cosTheta 2))
-1
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(- (pow alpha 2) 1)
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(pow alpha 2)
(* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(+ (* 2 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2))))) (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* -2 (/ (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))) (pow alpha 2)))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(+ (* 2 (* (PI) (log alpha))) (* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow alpha 2) (* (pow cosTheta 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(* (pow cosTheta 2) (+ (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2))) (* (pow alpha 2) (+ (* -2 (/ (* (PI) (log alpha)) (pow alpha 2))) (* 2 (* (PI) (log alpha)))))))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (* (pow cosTheta 2) (PI)))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(/ 1 (pow cosTheta 2))
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(pow cosTheta 2)
(* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log alpha)))) (* 1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log alpha)))))
(* -1/2 (/ (* (pow alpha 2) (+ 1 (pow cosTheta 2))) (* (PI) (log (/ 1 alpha)))))
(* (pow alpha 2) (+ (* -1/2 (/ (+ 1 (pow cosTheta 2)) (* (PI) (log (/ 1 alpha))))) (* 1/2 (/ (+ 1 (pow cosTheta 2)) (* (pow alpha 2) (* (PI) (log (/ 1 alpha))))))))
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(* -1 (log (/ 1 alpha)))
(* -1 (log (/ 1 alpha)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* 2 (log alpha))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ 1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* -2 (log (/ -1 alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* 2 (* (PI) (log alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)
(* -1 cosTheta)

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

eval42.0ms (0.4%)

Compiler: Compiled 19080 to 593 computations (96.9% saved)

prune52.0ms (0.5%)

Pruning

39 alts after pruning (35 fresh and 4 done)

	Pruned	Kept	Total
New	575	13	588
Fresh	3	22	25
Picked	3	2	5
Done	0	2	2
Total	581	39	620

Accuracy

100.0%

Counts

620 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 alpha alpha)))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
✓	-0.0%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	98.0%	(/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	97.6%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
	97.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
✓	98.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	95.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	97.8%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	83.0%	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	83.3%	(/.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	67.0%	(/.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 cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))
	67.0%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (/.f32 (+.f32 (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 3 binary32))) (+.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 alpha alpha) (.f32 #s(literal -2 binary32) (+.f32 (.f32 (neg.f32 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (*.f32 alpha alpha)))))))
	95.3%	(/.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 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.4%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (+.f32 alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	98.0%	(/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	65.9%	(/.f32 (.f32 #s(literal -1/2 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))
	1.8%	(/.f32 (neg.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 cosTheta cosTheta))
	95.0%	(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 4 binary32)))) (.f32 (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))
▶	1.8%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
	67.0%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (/.f32 (.f32 (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) #s(literal 2 binary32))) (*.f32 alpha alpha)))))
✓	96.6%	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.5%	(.f32 (/.f32 (/.f32 (.f32 (.f32 alpha alpha) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	66.0%	(.f32 (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.5%	(.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	96.2%	(.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (log.f32 (.f32 alpha alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	97.4%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (neg.f32 (log.f32 alpha))))) (/.f32 #s(literal -1/2 binary32) (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))

Compiler

Compiled 1917 to 1106 computations (42.3% saved)

simplify268.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)))
✓	cost-diff	32	(+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))
✓	cost-diff	32	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta)))
✓	cost-diff	32	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
✓	cost-diff	64	(+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta)))
✓	cost-diff	64	(.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (.f32 cosTheta cosTheta))))
✓	cost-diff	64	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
✓	cost-diff	128	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #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)) (PI.f32))
✓	cost-diff	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	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 (.f32 alpha (*.f32 alpha alpha)))
✓	cost-diff	0	(+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) #s(literal -1 binary32))
✓	cost-diff	384	(.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
✓	cost-diff	384	(/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))

Rules

3674×	`-lowering-.f32`
3674×	`-lowering-.f64`
1800×	`sum3-define`
1668×	`/-lowering-/.f32`
1668×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	343
1	142	315
2	464	308
3	2035	285
4	6507	285
0	8528	285

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize286.0ms (2.7%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.2%	(.f32 alpha (.f32 alpha alpha))
✓	accuracy	99.1%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (neg.f32 cosTheta) cosTheta))))
✓	accuracy	98.8%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	accuracy	98.4%	(/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha)))
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.4%	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
✓	accuracy	98.8%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
✓	accuracy	98.8%	(/.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)))
✓	accuracy	99.8%	(+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.1%	(/.f32 (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))
✓	accuracy	98.9%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	accuracy	100.0%	(PI.f32)
✓	accuracy	99.7%	(/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
✓	accuracy	99.3%	(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
✓	accuracy	99.2%	(.f32 (PI.f32) (.f32 cosTheta cosTheta))
✓	accuracy	99.4%	(.f32 alpha (.f32 alpha (*.f32 alpha alpha)))
✓	accuracy	99.2%	(.f32 alpha (.f32 alpha alpha))
✓	accuracy	98.9%	(/.f32 (.f32 (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
✓	accuracy	98.6%	(.f32 (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))

Results

197.0ms

256×

valid

Compiler

Compiled 417 to 43 computations (89.7% saved)

Precisions

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

ival-mult: 27.0ms (42% of total)

ival-div: 17.0ms (26.5% of total)

ival-add: 8.0ms (12.5% of total)

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

ival-sub: 2.0ms (3.1% of total)

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

const: 1.0ms (1.6% of total)

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

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

series51.0ms (0.5%)

Counts

26 → 384

Calls

Call 1

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

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

Calls

96 calls:

Time	Variable		Point	Expression
23.0ms	cosTheta	@	0	(/ (/ (- 1 (* alpha (* alpha (* alpha alpha)))) (- -1 (* alpha alpha))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (neg cosTheta) cosTheta))))
9.0ms	cosTheta	@	0	(/ 1/2 (* (log alpha) (* (PI) (* cosTheta cosTheta))))
1.0ms	cosTheta	@	inf	(/ (* (+ (* alpha (* alpha (* alpha alpha))) -1) (/ 1 (* (+ (* alpha alpha) 1) (PI)))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	alpha	@	inf	(/ (* (+ (* alpha (* alpha (* alpha alpha))) -1) (/ 1 (* (+ (* alpha alpha) 1) (PI)))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
1.0ms	alpha	@	0	(/ (* (+ (* alpha (* alpha (* alpha alpha))) -1) (/ 1 (* (+ (* alpha alpha) 1) (PI)))) (* (log (* alpha alpha)) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite418.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3104×	`-lowering-.f32`
3104×	`-lowering-.f64`
2668×	`/-lowering-/.f32`
2668×	`/-lowering-/.f64`
2278×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	205
1	314	167
2	2726	166
0	8672	166

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 1452

Calls

Call 1

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

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

simplify333.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

4420×	`-lowering-.f32`
4420×	`-lowering-.f64`
2864×	`/-lowering-/.f32`
2864×	`/-lowering-/.f64`
1868×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	7171
1	1509	5651
2	6751	5641
0	8185	5641

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

eval322.0ms (3%)

Compiler: Compiled 89755 to 5647 computations (93.7% saved)

prune510.0ms (4.8%)

Pruning

38 alts after pruning (33 fresh and 5 done)

	Pruned	Kept	Total
New	2582	24	2606
Fresh	21	9	30
Picked	4	1	5
Done	0	4	4
Total	2607	38	2645

Accuracy

100.0%

Counts

2645 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.8%	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
	95.4%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (-.f32 #s(literal 0 binary32) (.f32 alpha alpha))))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.1%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
✓	-0.0%	(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
	97.5%	(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32))))
	97.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	95.2%	(/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (-.f32 #s(literal -1 binary32) (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	95.2%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (PI.f32))
	95.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (PI.f32) (log.f32 (E.f32)))) (log.f32 (*.f32 alpha alpha)))
✓	98.6%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	95.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.3%	(/.f32 (/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	95.4%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (log.f32 (.f32 alpha alpha)))
	95.1%	(/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	67.0%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	67.0%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	67.1%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	65.6%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	94.8%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32))) (log.f32 (.f32 alpha alpha)))
	98.0%	(/.f32 (.f32 (.f32 (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))) alpha) alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	95.0%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) (.f32 alpha alpha))))) (log.f32 (*.f32 alpha alpha)))
	65.9%	(/.f32 (.f32 #s(literal -1/2 binary32) (+.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (log.f32 alpha)))
	95.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32))))
	95.1%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (+.f32 (*.f32 alpha alpha) #s(literal -1 binary32))))
	65.6%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	97.8%	(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (.f32 (.f32 cosTheta cosTheta) (.f32 cosTheta cosTheta)))) (+.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))
✓	96.6%	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	66.0%	(.f32 (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	95.3%	(.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))
	96.5%	(.f32 (/.f32 (+.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha))) (+.f32 (*.f32 cosTheta cosTheta) #s(literal 1 binary32)))
	94.9%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (PI.f32)))
	95.1%	(.f32 (/.f32 (+.f32 alpha #s(literal 1 binary32)) (PI.f32)) (/.f32 (+.f32 alpha #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	97.6%	(.f32 (-.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))

Compiler

Compiled 2537 to 789 computations (68.9% saved)

regimes97.0ms (0.9%)

Counts

79 → 1

Calls

Call 1

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

Outputs

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

26.0ms	(/.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))))
22.0ms	(*.f32 alpha alpha)
22.0ms	alpha
21.0ms	cosTheta

Results

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

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes44.0ms (0.4%)

Counts

45 → 1

Calls

Call 1

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

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

Calls

3 calls:

14.0ms	(*.f32 alpha alpha)
14.0ms	alpha
13.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.9%	1	`cosTheta`
97.9%	1	`alpha`
97.9%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes31.0ms (0.3%)

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	alpha
10.0ms	cosTheta
8.0ms	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes31.0ms (0.3%)

Counts

28 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	(*.f32 alpha alpha)
8.0ms	alpha
8.0ms	cosTheta

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes31.0ms (0.3%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

3 calls:

11.0ms	(*.f32 alpha alpha)
10.0ms	cosTheta
8.0ms	alpha

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes26.0ms (0.2%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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)

regimes25.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	alpha
3.0ms	(*.f32 alpha alpha)
3.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.3%	1	`alpha`
95.3%	1	`(*.f32 alpha alpha)`
95.3%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes13.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

9.0ms	alpha
2.0ms	cosTheta
1.0ms	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`*-commutative_binary32`
16×	`+-commutative_binary32`
10×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	145
1	73	145
2	82	145
3	90	145
4	92	145

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.2s (20.6%)

Rules

7072×	`-lowering-.f32`
7072×	`-lowering-.f64`
5948×	`-lowering-.f32`
5948×	`-lowering-.f64`
5666×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	205
1	314	167
2	2726	166
0	8672	166
0	21	92
1	158	89
2	1257	89
0	8991	89
0	436	7171
1	1509	5651
2	6751	5641
0	8185	5641
0	712	9863
1	2539	7842
0	8849	7842
0	539	7615
1	1990	6341
0	8251	6341
0	224	4283
1	731	3519
2	2928	3443
0	8798	3443

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 440 to 243 computations (44.8% saved)

preprocess118.0ms (1.1%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1074 to 510 computations (52.5% saved)

analyze117.0ms (1.1%)

sample1.8s (16.6%)

preprocess215.0ms (2%)

explain147.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify166.0ms (1.6%)

localize104.0ms (1%)

series67.0ms (0.6%)

rewrite434.0ms (4.1%)

simplify353.0ms (3.3%)

eval128.0ms (1.2%)

prune187.0ms (1.8%)

simplify12.0ms (0.1%)

localize394.0ms (3.7%)

series47.0ms (0.4%)

rewrite22.0ms (0.2%)

simplify505.0ms (4.7%)

eval119.0ms (1.1%)

prune70.0ms (0.7%)

simplify11.0ms (0.1%)

localize312.0ms (2.9%)

series107.0ms (1%)

rewrite22.0ms (0.2%)

simplify435.0ms (4.1%)

eval42.0ms (0.4%)

prune52.0ms (0.5%)

simplify268.0ms (2.5%)

localize286.0ms (2.7%)

series51.0ms (0.5%)

rewrite418.0ms (3.9%)

simplify333.0ms (3.1%)

eval322.0ms (3%)

prune510.0ms (4.8%)

regimes97.0ms (0.9%)

regimes44.0ms (0.4%)

regimes31.0ms (0.3%)

regimes31.0ms (0.3%)

regimes31.0ms (0.3%)

regimes26.0ms (0.2%)

regimes25.0ms (0.2%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes13.0ms (0.1%)

simplify10.0ms (0.1%)

soundness2.2s (20.6%)

preprocess118.0ms (1.1%)

end0.0ms (0%)

Profiling