Metrics for GTR1 distribution

analyze86.0ms (0.9%)

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: 51.0ms

ival-mult: 16.0ms (31.6% of total)

...c/correct-round.rkt:119:19: 8.0ms (15.8% of total)

ival-log: 7.0ms (13.8% of total)

ival-<=: 7.0ms (13.8% of total)

ival-div: 3.0ms (5.9% of total)

ival-add: 3.0ms (5.9% of total)

ival-sub: 3.0ms (5.9% of total)

ival-pi: 2.0ms (3.9% of total)

ival-and: 2.0ms (3.9% of total)

const: 1.0ms (2% of total)

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

sample1.7s (17.5%)

Results

1.4s

8256×

valid

Precisions

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

ival-mult: 303.0ms (28.7% of total)

...c/correct-round.rkt:119:19: 176.0ms (16.6% of total)

ival-log: 139.0ms (13.1% of total)

ival-div: 120.0ms (11.3% of total)

ival-<=: 115.0ms (10.9% of total)

ival-sub: 58.0ms (5.5% of total)

ival-add: 57.0ms (5.4% of total)

ival-pi: 40.0ms (3.8% of total)

ival-and: 34.0ms (3.2% of total)

const: 13.0ms (1.2% of total)

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

Bogosity

preprocess247.0ms (2.5%)

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	181	116
2	695	114
3	3800	114
0	13	21
1	46	19
2	163	19
3	687	19
4	2890	19
5	6015	19
0	8027	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)) (log.f32 (*.f32 alpha alpha))) (*.f32 (PI.f32) (+.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) (* (PI) (fma (+ (square alpha) -1) (square cosTheta) 1))) (log (square alpha)))
(/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta)))))
(/ (/ (+ (square alpha) -1) (* (PI) (fma (+ (square alpha) -1) (square cosTheta) 1))) (log (square alpha)))
(/ (- (* (neg alpha) (neg alpha)) 1) (* (* (PI) (log (* (neg alpha) (neg alpha)))) (+ 1 (* (* (- (* (neg alpha) (neg alpha)) 1) cosTheta) cosTheta))))
(/ (/ (+ (square alpha) -1) (* (PI) (fma (+ (square alpha) -1) (square cosTheta) 1))) (log (square alpha)))
(neg (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) (neg cosTheta)) (neg cosTheta))))))
(/ (/ (+ (square alpha) -1) (PI)) (* (log (square alpha)) (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) (PI)) (* (log (square alpha)) (fnmsub (+ (square alpha) -1) (square cosTheta) 1)))
(/ (- (* cosTheta cosTheta) 1) (* (* (PI) (log (* cosTheta cosTheta))) (+ 1 (* (* (- (* cosTheta cosTheta) 1) alpha) alpha))))
(/ (+ (square cosTheta) -1) (* (log (square cosTheta)) (* (PI) (fma alpha (fmsub alpha (square cosTheta) alpha) 1))))

Symmetry

(abs cosTheta)

(abs alpha)

explain453.0ms (4.6%)

FPErrors

Click to see full error table

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

Results

375.0ms

512×

valid

Compiler

Compiled 214 to 41 computations (80.8% saved)

Precisions

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

ival-mult: 21.0ms (41.7% of total)

ival-add: 9.0ms (17.9% of total)

ival-div: 8.0ms (15.9% of total)

ival-log: 7.0ms (13.9% of total)

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

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

const: 1.0ms (2% 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
▶	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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

▶

98.5%

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

simplify301.0ms (3%)

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)) (log.f32 (.f32 alpha alpha)))
✓	cost-diff	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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

2512×	`-lowering-.f32`
2512×	`-lowering-.f64`
1726×	`+-lowering-+.f64`
1726×	`+-lowering-+.f32`
1448×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	146
1	73	140
2	232	140
3	1087	140
4	3705	139
5	6943	139
0	8054	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) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
(/ (+ (* alpha alpha) -1) (log (* alpha alpha)))
(+ (* alpha alpha) -1)
(* alpha alpha)
alpha
-1
(log (* alpha alpha))
(* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta))))
(PI)
(+ 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 alpha alpha) #s(literal -1 binary32)) (.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))))))
(- (* 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 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
(* (PI) (log (* alpha alpha)))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI)
(PI.f32)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
(+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
(* (* (- (* alpha alpha) 1) cosTheta) cosTheta)
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(* (- (* alpha alpha) 1) cosTheta)
(.f32 cosTheta (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))
cosTheta
(/ (/ (+ (* alpha alpha) -1) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
(/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.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))))))
(/ (+ (* alpha alpha) -1) (log (* alpha alpha)))
(/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.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)
(log (* alpha alpha))
(log.f32 (*.f32 alpha alpha))
(* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta))))
(.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta))))
(PI)
(PI.f32)
(+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))
(+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))
1
#s(literal 1 binary32)
(* (+ (* alpha alpha) -1) (* cosTheta cosTheta))
(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
(* cosTheta cosTheta)
(*.f32 cosTheta cosTheta)
cosTheta

localize106.0ms (1.1%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(log.f32 (*.f32 alpha alpha))
✓	accuracy	99.5%	(.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta))
✓	accuracy	99.0%	(/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha)))
✓	accuracy	98.7%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	accuracy	99.7%	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
✓	accuracy	99.4%	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
✓	accuracy	99.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	accuracy	98.9%	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Results

76.0ms

256×

valid

Compiler

Compiled 181 to 22 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 16.0ms (50.1% of total)

ival-div: 5.0ms (15.7% of total)

ival-log: 4.0ms (12.5% of total)

ival-add: 4.0ms (12.5% of total)

ival-sub: 2.0ms (6.3% of total)

ival-pi: 1.0ms (3.1% of total)

const: 1.0ms (3.1% of total)

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

series87.0ms (0.9%)

Counts

12 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
32.0ms	alpha	@	0	(* (PI) (log (* alpha alpha)))
14.0ms	cosTheta	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
8.0ms	alpha	@	0	(* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))
7.0ms	alpha	@	inf	(* (PI) (log (* alpha alpha)))
4.0ms	alpha	@	inf	(/ (+ (* alpha alpha) -1) (log (* alpha alpha)))

rewrite449.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3312×	`-lowering-.f32`
3312×	`-lowering-.f64`
2692×	`/-lowering-/.f32`
2692×	`/-lowering-/.f64`
1520×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	101
1	159	98
2	1264	98
0	8521	98

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 769

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

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

simplify324.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

5486×	`-lowering-.f32`
5486×	`-lowering-.f64`
2648×	`/-lowering-/.f32`
2648×	`/-lowering-/.f64`
1864×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4596
1	816	3764
2	3114	3679
0	8422	3679

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval116.0ms (1.2%)

Compiler: Compiled 52264 to 3058 computations (94.1% saved)

prune232.0ms (2.3%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	1269	23	1292
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1270	24	1294

Accuracy

99.9%

Counts

1294 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(/.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)))) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))) (PI.f32))
▶	98.0%	(/.f32 (/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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))))
	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
✓	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.1%	(/.f32 (/.f32 (+.f32 #s(literal -1 binary32) (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #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) cosTheta) (neg.f32 cosTheta)) cosTheta))))
▶	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	49.8%	(/.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))))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 #s(literal 2 binary32) (+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta)))))))
	98.4%	(/.f32 (+.f32 (/.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (log.f32 alpha)) (/.f32 #s(literal -1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	98.1%	(/.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))))
	98.2%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 alpha alpha)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 cosTheta cosTheta)))))
	98.5%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.8%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.7%	(+.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (log.f32 alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))

Compiler

Compiled 1334 to 750 computations (43.8% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	579

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize336.0ms (3.4%)

Localize:

Found 20 expressions of interest:

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

Results

249.0ms

256×

invalid

Compiler

Compiled 582 to 51 computations (91.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-mult: 33.0ms (36.6% of total)

ival-div: 28.0ms (31.1% of total)

ival-add: 14.0ms (15.5% of total)

ival-log: 8.0ms (8.9% of total)

ival-sub: 4.0ms (4.4% of total)

ival-pi: 1.0ms (1.1% of total)

const: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

series85.0ms (0.9%)

Counts

26 → 348

Calls

Call 1

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

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

Calls

102 calls:

Time	Variable		Point	Expression
17.0ms	alpha	@	-inf	(* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2))
5.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2)))
5.0ms	alpha	@	0	(* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2))
5.0ms	alpha	@	inf	(* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2))
4.0ms	cosTheta	@	0	(* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2))

rewrite26.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	329

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

26 → 26

Calls

Call 1

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

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

simplify410.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

6880×	`-lowering-.f32`
6880×	`-lowering-.f64`
2732×	`+-lowering-+.f64`
2732×	`+-lowering-+.f32`
1932×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	623	8702
1	2303	7088
0	8615	7088

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 348

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))))))))
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(* -2 (* (PI) (log (/ 1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)
(pow alpha 3)

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

eval55.0ms (0.5%)

Compiler: Compiled 25670 to 741 computations (97.1% saved)

prune64.0ms (0.6%)

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	688	14	702
Fresh	7	11	18
Picked	3	2	5
Done	0	1	1
Total	698	28	726

Accuracy

100.0%

Counts

726 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.9%	(/.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)))) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))) (PI.f32))
	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))))
▶	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	98.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (.f32 cosTheta cosTheta)))))
✓	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	98.1%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	1.8%	(/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
▶	48.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (/.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) cosTheta) (/.f32 (log.f32 alpha) cosTheta)))))
	49.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (+.f32 (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (/.f32 (log.f32 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.4%	(/.f32 (+.f32 (/.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (log.f32 alpha)) (/.f32 #s(literal -1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.5%	(/.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))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha (.f32 alpha (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	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 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
▶	66.8%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	97.6%	(+.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	97.3%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
	97.3%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1393 to 839 computations (39.8% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
26×	`/-lowering-/.f32`
26×	`/-lowering-/.f64`
10×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	453

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize252.0ms (2.5%)

Localize:

Found 20 expressions of interest:

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

Results

171.0ms

256×

invalid

Compiler

Compiled 456 to 49 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 28.0ms (39.7% of total)

ival-div: 20.0ms (28.3% of total)

ival-log: 8.0ms (11.3% of total)

ival-add: 8.0ms (11.3% of total)

ival-sub: 5.0ms (7.1% of total)

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

const: 1.0ms (1.4% of total)

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

series54.0ms (0.5%)

Counts

23 → 288

Calls

Call 1

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

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

87 calls:

Time	Variable		Point	Expression
20.0ms	cosTheta	@	inf	(/ -1 (* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2)))
3.0ms	alpha	@	-inf	(/ -1 (* (* (PI) (log alpha)) (* (- 1 (* cosTheta cosTheta)) 2)))
2.0ms	alpha	@	inf	(/ 1 (+ (* alpha alpha) -1))
2.0ms	alpha	@	-inf	(/ (- (* alpha alpha) 1) (* (* cosTheta cosTheta) (+ (* (PI) (* (log alpha) -2)) (* (/ (* 2 (PI)) cosTheta) (/ (log alpha) cosTheta)))))
2.0ms	alpha	@	inf	(/ (/ (+ (* alpha alpha) -1) (* (log alpha) 2)) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite27.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
26×	`/-lowering-/.f32`
26×	`/-lowering-/.f64`
10×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	240

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 23

Calls

Call 1

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

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

simplify359.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

4798×	`-lowering-.f32`
4798×	`-lowering-.f64`
3036×	`/-lowering-/.f32`
3036×	`/-lowering-/.f64`
1554×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	441	5984
1	1546	5136
2	6207	5090
0	8225	5090

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

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

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

eval36.0ms (0.4%)

Compiler: Compiled 14875 to 560 computations (96.2% saved)

prune45.0ms (0.5%)

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	514	10	524
Fresh	3	17	20
Picked	4	1	5
Done	0	3	3
Total	521	31	552

Accuracy

100.0%

Counts

552 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(/.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)))) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.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)) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #s(literal 1 binary32)) (PI.f32))
	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))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
▶	98.4%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
✓	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
▶	96.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
▶	97.4%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(literal -1 binary32) cosTheta) cosTheta))))
	81.4%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 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))))
	89.3%	(/.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (.f32 (.f32 alpha alpha) (+.f32 #s(literal -1 binary32) (-.f32 #s(literal 0 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))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	49.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)) (/.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)))))
✓	48.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (/.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) cosTheta) (/.f32 (log.f32 alpha) cosTheta)))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	98.4%	(/.f32 (+.f32 (/.f32 (.f32 (.f32 alpha alpha) #s(literal 1/2 binary32)) (log.f32 alpha)) (/.f32 #s(literal -1/2 binary32) (log.f32 alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	97.5%	(/.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))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha (.f32 alpha (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	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 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	98.3%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	33.4%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (/.f32 (.f32 #s(literal 2 binary32) (PI.f32)) cosTheta) (/.f32 (log.f32 alpha) cosTheta)))))
	97.6%	(+.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	97.3%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))
	97.3%	(.f32 #s(literal 1/2 binary32) (.f32 (+.f32 (.f32 cosTheta cosTheta) #s(literal 1 binary32)) (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (*.f32 (PI.f32) (log.f32 alpha)))))

Compiler

Compiled 1530 to 926 computations (39.5% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

32×	`/-lowering-/.f32`
32×	`/-lowering-/.f64`
24×	`-lowering-.f32`
24×	`-lowering-.f64`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	516

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Calls

Call 1

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

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

localize308.0ms (3.1%)

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

Results

231.0ms

256×

invalid

Compiler

Compiled 519 to 42 computations (91.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-div: 26.0ms (39.5% of total)

ival-mult: 20.0ms (30.4% of total)

ival-add: 9.0ms (13.7% of total)

ival-log: 8.0ms (12.2% of total)

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

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

const: 1.0ms (1.5% of total)

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

series33.0ms (0.3%)

Counts

23 → 252

Calls

Call 1

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

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

Calls

72 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta	@	inf	(/ (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
3.0ms	alpha	@	inf	(/ (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
2.0ms	alpha	@	0	(/ (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
2.0ms	alpha	@	-inf	(/ (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))
2.0ms	cosTheta	@	0	(/ (/ (/ (- (* (* alpha (* alpha (* alpha alpha))) (+ (* alpha alpha) 1)) (+ (* alpha alpha) 1)) (* (+ (* alpha alpha) 1) (+ (* alpha alpha) 1))) (log (* alpha alpha))) (* (PI) (+ 1 (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)))))

rewrite26.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

32×	`/-lowering-/.f32`
32×	`/-lowering-/.f64`
24×	`-lowering-.f32`
24×	`-lowering-.f64`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	305

Stop Event

1×	iter limit
1×	iter limit
1×	unsound

Counts

23 → 23

Calls

Call 1

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

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

simplify640.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

5688×	`-lowering-.f32`
5688×	`-lowering-.f64`
3670×	`/-lowering-/.f32`
3670×	`/-lowering-/.f64`
3194×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	567	7517
1	2036	6162
0	8466	6162

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

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

Outputs
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(*.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 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 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))

eval52.0ms (0.5%)

Compiler: Compiled 22167 to 634 computations (97.1% saved)

prune53.0ms (0.5%)

Pruning

31 alts after pruning (27 fresh and 4 done)

	Pruned	Kept	Total
New	554	11	565
Fresh	6	16	22
Picked	4	1	5
Done	1	3	4
Total	565	31	596

Accuracy

100.0%

Counts

596 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.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)))) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
	-0.0%	(/.f32 (/.f32 (/.f32 #s(literal -1 binary32) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))) #s(literal 1 binary32)) (PI.f32))
	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))))
	97.8%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 (log.f32 alpha) #s(literal 2 binary32))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 cosTheta cosTheta)))))
✓	98.5%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	96.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))
✓	96.1%	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
	96.0%	(/.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)))
	97.4%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 cosTheta) cosTheta))))
	81.3%	(/.f32 (/.f32 #s(literal 1 binary32) (neg.f32 (+.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))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	66.8%	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	65.9%	(/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (.f32 (/.f32 (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha))) alpha) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) 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) cosTheta) (neg.f32 cosTheta)) cosTheta))))
✓	97.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	49.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal -2 binary32)) (/.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta)))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
	96.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	97.5%	(/.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))))
	97.9%	(/.f32 (.f32 (+.f32 alpha #s(literal 1 binary32)) (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	95.8%	(/.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)))
	97.9%	(/.f32 (.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha (.f32 alpha (-.f32 #s(literal 0 binary32) (log.f32 alpha))))) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)))) (.f32 (PI.f32) (+.f32 #s(literal 1 binary32) (.f32 (+.f32 (.f32 alpha alpha) #s(literal -1 binary32)) (.f32 cosTheta cosTheta)))))
	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 alpha)) (.f32 (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)) #s(literal 2 binary32))))
	98.3%	(/.f32 (.f32 alpha (.f32 alpha (+.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) (.f32 alpha alpha))))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	66.8%	(/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	65.9%	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
	33.4%	(/.f32 #s(literal -1 binary32) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) #s(literal -2 binary32))) (.f32 (/.f32 (.f32 #s(literal 2 binary32) (PI.f32)) cosTheta) (/.f32 (log.f32 alpha) cosTheta)))))
	96.2%	(+.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 alpha))) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))))
	97.1%	(.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)))
	97.3%	(.f32 (.f32 alpha alpha) (+.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))) (/.f32 #s(literal -1/2 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (-.f32 #s(literal 0 binary32) (log.f32 alpha)))))))

Compiler

Compiled 2160 to 700 computations (67.6% saved)

regimes148.0ms (1.5%)

Counts

60 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

92.0ms	cosTheta
18.0ms	(/.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))))
17.0ms	(*.f32 alpha alpha)
16.0ms	alpha

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)

regimes59.0ms (0.6%)

Counts

33 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

12.0ms	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
10.0ms	cosTheta
9.0ms	(*.f32 alpha alpha)
9.0ms	alpha

Results

Accuracy	Segments	Branch
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)`
98.6%	1	`cosTheta`

Compiler

Compiled 37 to 20 computations (45.9% saved)

regimes39.0ms (0.4%)

Counts

29 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

regimes20.0ms (0.2%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes50.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.3%	1	`alpha`
96.3%	1	`(*.f32 alpha alpha)`
96.3%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes10.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
66.8%	1	`cosTheta`
66.8%	1	`alpha`
66.8%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
65.9%	1	`cosTheta`
65.9%	1	`alpha`
65.9%	1	`(*.f32 alpha alpha)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes28.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

22.0ms	cosTheta
2.0ms	(*.f32 alpha alpha)
2.0ms	alpha

Results

Accuracy	Segments	Branch
65.9%	1	`alpha`
65.9%	1	`(*.f32 alpha alpha)`
65.9%	1	`cosTheta`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

34×	`*-commutative_binary32`
18×	`+-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	48	129
1	79	129
2	88	129
3	95	129
4	96	129

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

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

soundness2.5s (24.8%)

Rules

6880×	`-lowering-.f32`
6880×	`-lowering-.f64`
5688×	`-lowering-.f32`
5688×	`-lowering-.f64`
5486×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	567	7517
1	2036	6162
0	8466	6162
0	21	101
1	159	98
2	1264	98
0	8521	98
0	240	4596
1	816	3764
2	3114	3679
0	8422	3679
0	13	21
1	46	19
2	163	19
3	687	19
4	2890	19
5	6015	19
0	8027	19
0	623	8702
1	2303	7088
0	8615	7088
0	441	5984
1	1546	5136
2	6207	5090
0	8225	5090

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 422 to 246 computations (41.7% saved)

preprocess51.0ms (0.5%)

Remove

(abs alpha)

(abs cosTheta)

Compiler

Compiled 1042 to 536 computations (48.6% saved)

analyze86.0ms (0.9%)

sample1.7s (17.5%)

preprocess247.0ms (2.5%)

explain453.0ms (4.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify301.0ms (3%)

localize106.0ms (1.1%)

series87.0ms (0.9%)

rewrite449.0ms (4.5%)

simplify324.0ms (3.3%)

eval116.0ms (1.2%)

prune232.0ms (2.3%)

simplify18.0ms (0.2%)

localize336.0ms (3.4%)

series85.0ms (0.9%)

rewrite26.0ms (0.3%)

simplify410.0ms (4.1%)

eval55.0ms (0.5%)

prune64.0ms (0.6%)

simplify16.0ms (0.2%)

localize252.0ms (2.5%)

series54.0ms (0.5%)

rewrite27.0ms (0.3%)

simplify359.0ms (3.6%)

eval36.0ms (0.4%)

prune45.0ms (0.5%)

simplify15.0ms (0.2%)

localize308.0ms (3.1%)

series33.0ms (0.3%)

rewrite26.0ms (0.3%)

simplify640.0ms (6.4%)

eval52.0ms (0.5%)

prune53.0ms (0.5%)

regimes148.0ms (1.5%)

regimes59.0ms (0.6%)

regimes39.0ms (0.4%)

regimes20.0ms (0.2%)

regimes50.0ms (0.5%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes28.0ms (0.3%)

regimes7.0ms (0.1%)

simplify16.0ms (0.2%)

soundness2.5s (24.8%)

preprocess51.0ms (0.5%)

end0.0ms (0%)

Profiling