Metrics for GTR1 distribution

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze59.0ms (0.8%)

Memory

38.6MiB live, 129.1MiB allocated; 10ms collecting garbage

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 40 to 23 computations (42.5% saved)

sample2.3s (30.4%)

Memory

-172.5MiB live, 2 078.7MiB allocated; 1.5s collecting garbage

Samples

1.3s

8 256×

valid

Precisions

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

ival-mult: 351.0ms (33.2% of total)

ival-add: 146.0ms (13.8% of total)

const: 141.0ms (13.3% of total)

ival-<=: 120.0ms (11.4% of total)

ival-log: 107.0ms (10.1% of total)

ival-div: 82.0ms (7.8% of total)

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

ival-pi: 29.0ms (2.7% of total)

ival-and: 25.0ms (2.4% of total)

exact: 10.0ms (0.9% of total)

adjust: 3.0ms (0.3% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain192.0ms (2.5%)

Memory

25.6MiB live, 274.0MiB allocated; 21ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
1	-	-	`(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))`
1	-	-	`(log.f32 (*.f32 alpha alpha))`
0	-	-	`(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))`
0	-	-	`(PI.f32)`
0	-	-	`#s(literal 1 binary32)`
0	-	-	`cosTheta`
0	-	-	`alpha`
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))))`
0	-	-	`(.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)))`
0	-	-	`(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)`
0	-	-	`(*.f32 alpha alpha)`
0	-	-	`(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)`
0	-	-	`(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f32`	`(log.f32 (*.f32 alpha alpha))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	0	0
-	1	255

Precision

0.0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	1	0	255

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	1	0	0

Precision?

0.0

Recall?

0/0

Samples

46.0ms

512×

valid

Compiler

Compiled 210 to 43 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 15.0ms (48.6% of total)

ival-log: 5.0ms (16.2% of total)

ival-div: 3.0ms (9.7% of total)

ival-pi: 2.0ms (6.5% of total)

ival-add: 2.0ms (6.5% of total)

ival-sub: 2.0ms (6.5% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess134.0ms (1.8%)

Memory

-7.0MiB live, 127.4MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	122
1	152	122
2	595	122
3	3333	120
0	13	24
0	23	24
1	55	24
2	221	24
3	1191	24
4	4601	24
0	8344	21

Stop Event

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

Calls

Call 1

Inputs

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

Outputs

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

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

Symmetry

(abs alpha)

(abs cosTheta)

Compiler

Compiled 24 to 13 computations (45.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.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 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 24 to 13 computations (45.8% saved)

simplify120.0ms (1.6%)

Memory

-4.4MiB live, 98.4MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 alpha alpha)
cost-diff	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))))
cost-diff	1	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	91
0	23	91
1	55	91
2	221	91
3	1191	91
4	4601	91
0	8344	81

Stop Event

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

Calls

Call 1

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

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

localize69.0ms (0.9%)

Memory

3.1MiB live, 47.8MiB allocated; 4ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.12109375	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.203125	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.3203125	(/.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	0.390625	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

23.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 7.0ms (46.3% of total)

ival-log: 3.0ms (19.8% of total)

ival-div: 2.0ms (13.2% of total)

ival-pi: 1.0ms (6.6% of total)

ival-add: 1.0ms (6.6% of total)

ival-sub: 1.0ms (6.6% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series72.0ms (0.9%)

Memory

18.2MiB live, 64.1MiB allocated; 3ms collecting garbage

Counts

7 → 43

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
47.0ms	alpha	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
9.0ms	alpha	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
8.0ms	alpha	@	-inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
3.0ms	cosTheta	@	inf	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))
3.0ms	cosTheta	@	0	((- (* alpha alpha) 1) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* alpha alpha) (* (PI) (log (* alpha alpha))) (* (- (* alpha alpha) 1) cosTheta) (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))

simplify199.0ms (2.6%)

Memory

-12.8MiB live, 130.1MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1450
1	572	1398
2	2417	1236
0	8614	1182

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 43

Calls

Call 1

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

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

rewrite211.0ms (2.8%)

Memory

19.5MiB live, 208.0MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55

Stop Event

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

Counts

7 → 372

Calls

Call 1

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

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

eval115.0ms (1.5%)

Memory: -43.6MiB live, 101.5MiB allocated; 15ms collecting garbage
Compiler: Compiled 19 163 to 2 092 computations (89.1% saved)

prune35.0ms (0.5%)

Memory

3.0MiB live, 50.5MiB allocated; 1ms collecting garbage

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	483	24	507
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	484	24	508

Accuracy

100.0%

Counts

508 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.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))))
	98.3%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.1%	(/.f32 (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	97.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	97.8%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 (fma.f32 alpha alpha #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))))
	98.4%	(/.f32 (-.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32)))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
▶	98.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #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))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	68.0%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	97.2%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
	97.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	94.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 1 632 to 946 computations (42% saved)

simplify9.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(*.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)))
cost-diff	0	(/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
cost-diff	0	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
cost-diff	0	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
cost-diff	0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
cost-diff	0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
cost-diff	0	(.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	548
0	92	548

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

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

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

localize211.0ms (2.8%)

Memory

19.9MiB live, 162.1MiB allocated; 13ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)))
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 cosTheta cosTheta)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32)))
accuracy	0.0	(.f32 (PI.f32) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
accuracy	0.0	(*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	(cbrt.f32 (PI.f32))
accuracy	29.98788023102775	(PI.f32)

Samples

175.0ms

256×

invalid

Compiler

Compiled 579 to 53 computations (90.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-mult: 65.0ms (42.4% of total)

ival-add: 56.0ms (36.5% of total)

ival-div: 9.0ms (5.9% of total)

ival-log: 7.0ms (4.6% of total)

ival-pow: 7.0ms (4.6% of total)

ival-sub: 3.0ms (2% of total)

ival-pow2: 2.0ms (1.3% of total)

ival-pi: 1.0ms (0.7% of total)

ival-cbrt: 1.0ms (0.7% of total)

exact: 1.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series313.0ms (4.1%)

Memory

-5.5MiB live, 270.7MiB allocated; 32ms collecting garbage

Counts

23 → 136

Calls

Call 1

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

Outputs
(* 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)))))))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
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(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
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-1
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1
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(+ 1 (* (pow alpha 2) (- (* alpha (- (pow alpha 2) 1)) 1)))
(log alpha)
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* 2 (log alpha))
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(* (pow alpha 2) (- 1 (/ 1 (pow alpha 2))))
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(* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI))))
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(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
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(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(- (+ (/ 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 (/ (+ (* -1 (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 5))) (/ 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 (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 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(* -1 (log (/ 1 alpha)))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* -2 (log (/ 1 alpha)))
(* -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)))))))))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 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))))))
(* -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)))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -2 (log (/ -1 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))

Calls

6 calls:

Time	Variable		Point	Expression
91.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (PI) (cbrt (PI)) (log alpha) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (log (pow (* alpha alpha) (PI))) (* (PI) (log (* alpha alpha))))
67.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (PI) (cbrt (PI)) (log alpha) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (log (pow (* alpha alpha) (PI))) (* (PI) (log (* alpha alpha))))
53.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (PI) (cbrt (PI)) (log alpha) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (log (pow (* alpha alpha) (PI))) (* (PI) (log (* alpha alpha))))
45.0ms	cosTheta	@	-inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (PI) (cbrt (PI)) (log alpha) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (log (pow (* alpha alpha) (PI))) (* (PI) (log (* alpha alpha))))
39.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (PI) (cbrt (PI)) (log alpha) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* cosTheta cosTheta) (log (pow (* alpha alpha) (PI))) (* (PI) (log (* alpha alpha))))

simplify237.0ms (3.1%)

Memory

19.2MiB live, 218.2MiB allocated; 57ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	640	5538
1	2031	5157
0	8959	5042

Stop Event

1×	iter limit
1×	node limit

Counts

136 → 136

Calls

Call 1

Inputs
(* 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)))))))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (- (pow alpha 2) 1) (* (NAN) (PI)))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (NAN) (PI)))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (* (NAN) (PI))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (* (NAN) (PI)))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (* (NAN) (PI)))))) (/ (pow (- (pow alpha 2) 1) 2) (* (NAN) (PI))))) (/ (pow alpha 2) (* (NAN) (PI)))) (/ 1 (* (NAN) (PI))))
(* (NAN) (PI))
(+ (* (NAN) (PI)) (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))
(PI)
(+ (PI) (* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1))))
(/ (- (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)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(/ (- (pow alpha 2) 1) (log (pow (pow alpha 2) (PI))))
(- (+ (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (log (pow (pow alpha 2) (PI))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 3)) (log (pow (pow alpha 2) (PI)))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(- (+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 4)) (log (pow (pow alpha 2) (PI))))) (* -1 (/ (pow (- (pow alpha 2) 1) 3) (log (pow (pow alpha 2) (PI))))))) (/ (pow (- (pow alpha 2) 1) 2) (log (pow (pow alpha 2) (PI)))))) (/ (pow alpha 2) (log (pow (pow alpha 2) (PI))))) (/ 1 (log (pow (pow alpha 2) (PI)))))
(log (pow (pow alpha 2) (PI)))
(+ (log (pow (pow alpha 2) (PI))) (* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1))))
(/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))
(+ (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 4) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(* cosTheta (- (pow alpha 2) 1))
(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))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
(/ 1 (* (pow cosTheta 2) (* (NAN) (PI))))
(/ (- (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (NAN) (PI))) (/ 1 (* (pow cosTheta 4) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 2)))))) (+ (/ 1 (* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))) (/ 1 (* (pow cosTheta 6) (* (NAN) (* (PI) (pow (- (pow alpha 2) 1) 3))))))) (pow cosTheta 2))
(* (pow cosTheta 2) (* (NAN) (* (PI) (- (pow alpha 2) 1))))
(* (pow cosTheta 2) (+ (* (NAN) (* (PI) (- (pow alpha 2) 1))) (/ (* (NAN) (PI)) (pow cosTheta 2))))
(* (pow cosTheta 2) (* (PI) (- (pow alpha 2) 1)))
(* (pow cosTheta 2) (+ (* (PI) (- (pow alpha 2) 1)) (/ (PI) (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))
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(* (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))))
(/ 1 (* (pow cosTheta 2) (log (pow (pow alpha 2) (PI)))))
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(* (pow cosTheta 2) (* (log (pow (pow alpha 2) (PI))) (- (pow alpha 2) 1)))
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(/ (- (pow alpha 3) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
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-1
(- (pow alpha 2) 1)
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(/ -1 (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))))
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(* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2)))))
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(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (* -1 (* alpha (+ (* -1 (- (* 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))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (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
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* (pow alpha 2) (- (* -1 alpha) 1)))
(+ 1 (* (pow alpha 2) (- (* alpha (- (pow alpha 2) 1)) 1)))
(log alpha)
(* -1 cosTheta)
(+ (* -1 cosTheta) (* (pow alpha 2) cosTheta))
(* 2 (log alpha))
(/ -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)))))))
(* (pow alpha 2) (- 1 (/ 1 (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)))))
(- (/ 1 (* (pow cosTheta 2) (* (NAN) (PI)))) (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (NAN) (PI))))))
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(* (pow alpha 2) (* (pow cosTheta 2) (* (NAN) (PI))))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (* (NAN) (PI))) (/ (* (NAN) (* (PI) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2))))
(* (pow alpha 2) (* (pow cosTheta 2) (PI)))
(* (pow alpha 2) (+ (* (pow cosTheta 2) (PI)) (/ (* (PI) (+ 1 (* -1 (pow cosTheta 2)))) (pow alpha 2))))
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(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(* -1 (log (/ 1 alpha)))
(* (pow alpha 2) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(* -2 (log (/ 1 alpha)))
(* -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))))))))))
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(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 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))))))
(* -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)))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(* -2 (log (/ -1 alpha)))
(* -2 (* (PI) (log (/ -1 alpha))))

Outputs
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
(+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta) (.f32 #s(literal 1/2 binary32) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (log.f32 alpha) (PI.f32)))
(+ (* 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)))))))
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(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32)))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))))
(- (+ (* -1 (/ (* (+ 1 (* -1 (pow cosTheta 2))) (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (* (pow alpha 4) (pow cosTheta 2)))) (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))))))
(-.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 (log.f32 alpha) (PI.f32)))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (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 (fma.f32 (.f32 #s(literal 1/2 binary32) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 (log.f32 alpha) (PI.f32)))) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))) (fma.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha))))))
(- (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 5))) (/ 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 (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 (fma.f32 (/.f32 (.f32 #s(literal 0 binary32) (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 (log.f32 alpha) (PI.f32)))))) (pow.f32 alpha #s(literal 5 binary32))) #s(literal -1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta)) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))) (fma.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (neg.f32 (.f32 (log.f32 alpha) (PI.f32))))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (neg.f32 (log.f32 alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha))))))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(*.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(*.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))
(* -1 (log (/ 1 alpha)))
(log.f32 alpha)
(* (pow alpha 2) cosTheta)
(.f32 (.f32 alpha alpha) cosTheta)
(* (pow alpha 2) (+ cosTheta (* -1 (/ cosTheta (pow alpha 2)))))
(.f32 (.f32 (-.f32 cosTheta (/.f32 cosTheta (*.f32 alpha alpha))) alpha) alpha)
(* -2 (log (/ 1 alpha)))
(neg.f32 (*.f32 #s(literal -2 binary32) (log.f32 alpha)))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) 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)))))))))
(-.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) 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)))))))))
(-.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 8 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (fma.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 (.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (*.f32 alpha alpha))))
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) 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 (fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) 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 (fma.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 (.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32))) (*.f32 alpha alpha))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(*.f32 (neg.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 5 binary32)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(*.f32 (neg.f32 (pow.f32 alpha #s(literal 5 binary32))) (-.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha) #s(literal 1 binary32)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(*.f32 (neg.f32 (pow.f32 alpha #s(literal 5 binary32))) (fma.f32 (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 3 binary32))) #s(literal -1 binary32) (-.f32 (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha) #s(literal 1 binary32))))
(+ (log -1) (* -1 (log (/ -1 alpha))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -2 (log (/ -1 alpha)))
(*.f32 (log.f32 (/.f32 #s(literal -1 binary32) alpha)) #s(literal -2 binary32))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))

rewrite49.0ms (0.6%)

Memory

-12.6MiB live, 45.1MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	297
0	92	297

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

23 → 24

Calls

Call 1

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

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

eval22.0ms (0.3%)

Memory: -7.1MiB live, 39.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 11 527 to 958 computations (91.7% saved)

prune31.0ms (0.4%)

Memory

1.2MiB live, 48.5MiB allocated; 2ms collecting garbage

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	194	22	216
Fresh	12	7	19
Picked	5	0	5
Done	0	0	0
Total	211	29	240

Accuracy

100.0%

Counts

240 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
▶	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	98.3%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	83.2%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	77.2%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	97.4%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	67.3%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
▶	43.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (/.f32 (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #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))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	96.3%	#s(approx (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
▶	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	94.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 2 446 to 1 496 computations (38.8% saved)

simplify9.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
cost-diff	0	(.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha)
cost-diff	0	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
cost-diff	0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
cost-diff	0	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
cost-diff	0	(PI.f32)
cost-diff	0	(/.f32 #s(literal -1/2 binary32) (PI.f32))
cost-diff	0	(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
cost-diff	0	(*.f32 (NAN.f32) (PI.f32))
cost-diff	0	#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
cost-diff	0	(fma.f32 alpha alpha #s(literal -1 binary32))
cost-diff	0	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
cost-diff	0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32)))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	658
0	114	651

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Calls

Call 1

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

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

localize251.0ms (3.3%)

Memory

-11.9MiB live, 200.7MiB allocated; 44ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 alpha alpha)
accuracy	0.0	(log.f32 (*.f32 alpha alpha))
accuracy	0.0	#s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 cosTheta cosTheta)
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(*.f32 (NAN.f32) (PI.f32))
accuracy	0.0	(NAN.f32)
accuracy	0.0	#s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32)))
accuracy	29.98788023102775	(PI.f32)
accuracy	0.0	(.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32)))))
accuracy	29.98788023102775	(PI.f32)

Samples

191.0ms

256×

invalid

Compiler

Compiled 536 to 58 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 153.0ms

ival-div: 67.0ms (43.8% of total)

ival-mult: 65.0ms (42.4% of total)

ival-add: 6.0ms (3.9% of total)

ival-log: 5.0ms (3.3% of total)

ival-sub: 4.0ms (2.6% of total)

ival-pow2: 2.0ms (1.3% of total)

ival-pi: 1.0ms (0.7% of total)

ival-cbrt: 1.0ms (0.7% of total)

exact: 1.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

ival-nan: 0.0ms (0% of total)

series98.0ms (1.3%)

Memory

32.1MiB live, 89.6MiB allocated; 30ms collecting garbage

Counts

23 → 101

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
48.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log alpha) (* 2 (+ (* (* (* cosTheta cosTheta) (PI)) (* (log alpha) (- (* alpha alpha) 1))) (* (log alpha) (PI)))) (NAN) (* cosTheta cosTheta) (log (* alpha alpha)))
17.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log alpha) (* 2 (+ (* (* (* cosTheta cosTheta) (PI)) (* (log alpha) (- (* alpha alpha) 1))) (* (log alpha) (PI)))) (NAN) (* cosTheta cosTheta) (log (* alpha alpha)))
16.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log alpha) (* 2 (+ (* (* (* cosTheta cosTheta) (PI)) (* (log alpha) (- (* alpha alpha) 1))) (* (log alpha) (PI)))) (NAN) (* cosTheta cosTheta) (log (* alpha alpha)))
5.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log alpha) (* 2 (+ (* (* (* cosTheta cosTheta) (PI)) (* (log alpha) (- (* alpha alpha) 1))) (* (log alpha) (PI)))) (NAN) (* cosTheta cosTheta) (log (* alpha alpha)))
4.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (/ (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0))) (+ (* alpha alpha) -1) (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (* (NAN) (PI)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (PI)) (PI) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (* (- 1 (/ 1 (* alpha alpha))) alpha) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log alpha) (* 2 (+ (* (* (* cosTheta cosTheta) (PI)) (* (log alpha) (- (* alpha alpha) 1))) (* (log alpha) (PI)))) (NAN) (* cosTheta cosTheta) (log (* alpha alpha)))

simplify263.0ms (3.4%)

Memory

-31.6MiB live, 201.9MiB allocated; 73ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	485	3852
1	1581	3637
2	7479	3381
0	8681	3320

Stop Event

1×	iter limit
1×	node limit

Counts

101 → 100

Calls

Call 1

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

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

rewrite17.0ms (0.2%)

Memory

25.2MiB live, 25.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	433
0	114	426

Stop Event

1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

23 → 24

Calls

Call 1

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

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

eval21.0ms (0.3%)

Memory: -12.0MiB live, 31.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 10 186 to 777 computations (92.4% saved)

prune28.0ms (0.4%)

Memory

20.7MiB live, 66.4MiB allocated; 4ms collecting garbage

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	1	23	24
Picked	3	2	5
Done	0	0	0
Total	168	31	199

Accuracy

100.0%

Counts

199 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	96.9%	(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.7%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	83.2%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	77.2%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	97.4%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
▶	67.3%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
▶	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
▶	42.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (/.f32 (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
	94.8%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	98.2%	(/.f32 (.f32 (-.f32 alpha #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))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	97.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) 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))))
	96.3%	#s(approx (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
✓	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
▶	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
	67.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) cosTheta) cosTheta #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
▶	66.7%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	94.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 2 638 to 1 598 computations (39.4% saved)

simplify144.0ms (1.9%)

Memory

19.1MiB live, 202.7MiB allocated; 26ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	1	(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
cost-diff	1	(*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))
cost-diff	0	(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
cost-diff	0	(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(*.f32 (PI.f32) (log.f32 alpha))
cost-diff	0	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
cost-diff	0	#s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
cost-diff	0	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
cost-diff	0	(.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	649
0	119	616
1	257	580
2	922	580
3	6281	580
0	8006	577

Stop Event

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

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
(.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
(.f32 (PI.f32) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(PI.f32)
#s(approx (log (* alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32)))
(*.f32 (log.f32 alpha) #s(literal 2 binary32))
(log.f32 alpha)
#s(literal 2 binary32)
(fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))
(fma.f32 alpha alpha #s(literal -1 binary32))
#s(literal -1 binary32)
(*.f32 cosTheta cosTheta)
cosTheta
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
#s(literal -1/2 binary32)
(*.f32 (PI.f32) (log.f32 alpha))
(PI.f32)
(log.f32 alpha)
alpha
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
#s(literal 1/2 binary32)
(log.f32 alpha)
alpha
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
#s(literal 1 binary32)
(PI.f32)
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))))
#s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32))
#s(literal 1 binary32)
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))
(-.f32 alpha #s(literal 1 binary32))
alpha
(fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha))
(+.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 (PI.f32) (log.f32 (.f32 alpha alpha)))
(PI.f32)
(log.f32 (*.f32 alpha alpha))
(*.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)) cosTheta) cosTheta)
(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cosTheta
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(*.f32 alpha alpha)
alpha
#s(literal 1 binary32)
#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
(.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))
(.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32))
(*.f32 cosTheta cosTheta)
cosTheta
#s(literal 2 binary32)
(.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))
(PI.f32)
(fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))
(log.f32 alpha)
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
#s(literal -1 binary32)
(/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)
(/.f32 (log.f32 alpha) cosTheta)

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

localize187.0ms (2.4%)

Memory

5.1MiB live, 289.0MiB allocated; 28ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.22265625	(/.f32 (log.f32 alpha) cosTheta)
accuracy	0.3203125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
accuracy	10.672294866569574	#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy	17.695556224142255	(.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))
accuracy	0.3203125	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
accuracy	0.390625	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.4310150390737681	(*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))
accuracy	10.79672121255778	#s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32))
accuracy	0.30859375	(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
accuracy	0.34375	(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))
accuracy	0.4030075195368841	(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
accuracy	1.2109391519348736	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
accuracy	0.21484375	(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
accuracy	0.390625	(*.f32 (PI.f32) (log.f32 alpha))
accuracy	1.2091100137744673	#s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
accuracy	10.272679372137562	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
accuracy	0.03125	(.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
accuracy	0.07716752930532605	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
accuracy	0.3203125	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
accuracy	0.390625	(.f32 (PI.f32) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))

Samples

129.0ms

256×

valid

Compiler

Compiled 544 to 60 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-mult: 47.0ms (43.4% of total)

ival-div: 20.0ms (18.5% of total)

ival-sub: 20.0ms (18.5% of total)

ival-add: 7.0ms (6.5% of total)

ival-log: 5.0ms (4.6% of total)

ival-pow: 3.0ms (2.8% of total)

ival-pow2: 2.0ms (1.8% of total)

ival-pi: 1.0ms (0.9% of total)

ival-cbrt: 1.0ms (0.9% of total)

exact: 1.0ms (0.9% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series166.0ms (2.2%)

Memory

-33.0MiB live, 246.4MiB allocated; 52ms collecting garbage

Counts

23 → 126

Calls

Call 1

Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(*.f32 alpha alpha)
(.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(*.f32 (PI.f32) (log.f32 alpha))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
(.f32 (PI.f32) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))
#s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
(/.f32 (log.f32 alpha) cosTheta)

Outputs
(/ (- (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)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(* 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 (* (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
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))
(+ (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 4) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (log alpha) cosTheta)
(/ 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))
(* (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))))
(/ 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 (/ 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))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ (- (pow alpha 3) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))))))) (pow cosTheta 2))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
-1
(- (pow alpha 2) 1)
(/ -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))))))))
(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))))))
(- (* 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 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(* (PI) (log alpha))
(- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(/ 1/2 (log alpha))
(- (pow alpha 3) 1)
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (* -1 (* alpha (+ (* -1 (- (* 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))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (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 (PI))
(- (/ (pow alpha 2) (PI)) (/ 1 (PI)))
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* (pow alpha 2) (- (* -1 alpha) 1)))
(+ 1 (* (pow alpha 2) (- (* alpha (- (pow alpha 2) 1)) 1)))
(* 2 (* (pow cosTheta 2) (* (PI) (+ (* -1 (log alpha)) (/ (log alpha) (pow cosTheta 2))))))
(+ (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))) (* 2 (* (pow cosTheta 2) (* (PI) (+ (* -1 (log alpha)) (/ (log alpha) (pow cosTheta 2)))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 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))))))
(* -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)))))
(- (* 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 (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))))
(/ 1/2 (* (PI) (log (/ 1 alpha))))
(* -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)))))))
(/ -1/2 (log (/ 1 alpha)))
(pow alpha 3)
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(- (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 5))) (/ 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 (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))))))
(* -2 (* (PI) (log (/ 1 alpha))))
(/ (pow alpha 2) (PI))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (log (/ 1 alpha)) (* -1 (/ (log (/ 1 alpha)) (pow cosTheta 2)))))) (pow alpha 2)))))
(* -1 (/ (log (/ 1 alpha)) cosTheta))
(/ -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))))))
(* -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)))))
(/ 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 (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))))
(/ -1/2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 1/2 (/ (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(/ 1/2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (* -1 (+ (log -1) (* -1 (log (/ -1 alpha))))) (+ (* -1 (/ (log (/ -1 alpha)) (pow cosTheta 2))) (/ (log -1) (pow cosTheta 2)))))) (pow alpha 2)))))
(/ (+ (log -1) (* -1 (log (/ -1 alpha)))) cosTheta)

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	cosTheta	@	0	((- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (* (PI) (log alpha))) (* (PI) (log alpha)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (/ 1/2 (log alpha)) (/ (- (* alpha alpha) 1) (PI))) (/ 1/2 (log alpha)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (PI) (log (* alpha alpha))) (/ (- (* alpha alpha) 1) (PI)) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (PI) (log (* alpha alpha))) (* (* (* cosTheta cosTheta) 2) (* (PI) (+ (* (log alpha) (- (* alpha alpha) 1)) (/ (/ (log alpha) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (/ (log alpha) cosTheta))
34.0ms	alpha	@	0	((- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (* (PI) (log alpha))) (* (PI) (log alpha)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (/ 1/2 (log alpha)) (/ (- (* alpha alpha) 1) (PI))) (/ 1/2 (log alpha)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (PI) (log (* alpha alpha))) (/ (- (* alpha alpha) 1) (PI)) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (PI) (log (* alpha alpha))) (* (* (* cosTheta cosTheta) 2) (* (PI) (+ (* (log alpha) (- (* alpha alpha) 1)) (/ (/ (log alpha) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (/ (log alpha) cosTheta))
32.0ms	cosTheta	@	inf	((- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (* (PI) (log alpha))) (* (PI) (log alpha)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (/ 1/2 (log alpha)) (/ (- (* alpha alpha) 1) (PI))) (/ 1/2 (log alpha)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (PI) (log (* alpha alpha))) (/ (- (* alpha alpha) 1) (PI)) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (PI) (log (* alpha alpha))) (* (* (* cosTheta cosTheta) 2) (* (PI) (+ (* (log alpha) (- (* alpha alpha) 1)) (/ (/ (log alpha) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (/ (log alpha) cosTheta))
25.0ms	alpha	@	-inf	((- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (* (PI) (log alpha))) (* (PI) (log alpha)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (/ 1/2 (log alpha)) (/ (- (* alpha alpha) 1) (PI))) (/ 1/2 (log alpha)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (PI) (log (* alpha alpha))) (/ (- (* alpha alpha) 1) (PI)) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (PI) (log (* alpha alpha))) (* (* (* cosTheta cosTheta) 2) (* (PI) (+ (* (log alpha) (- (* alpha alpha) 1)) (/ (/ (log alpha) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (/ (log alpha) cosTheta))
22.0ms	alpha	@	inf	((- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/ -1/2 (* (PI) (log alpha))) (* (PI) (log alpha)) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (/ 1/2 (log alpha)) (/ (- (* alpha alpha) 1) (PI))) (/ 1/2 (log alpha)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (* (PI) (log (* alpha alpha))) (/ (- (* alpha alpha) 1) (PI)) (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (PI) (log (* alpha alpha))) (* (* (* cosTheta cosTheta) 2) (* (PI) (+ (* (log alpha) (- (* alpha alpha) 1)) (/ (/ (log alpha) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (/ (log alpha) cosTheta))

simplify183.0ms (2.4%)

Memory

41.9MiB live, 283.9MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	585	4828
1	1893	4453
0	8696	4349

Stop Event

1×	iter limit
1×	node limit

Counts

126 → 126

Calls

Call 1

Inputs
(/ (- (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)))))
(* (PI) (log (pow alpha 2)))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(* 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 (* (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
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))
(+ (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 4) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(* 2 (* (PI) (log alpha)))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(/ (log alpha) cosTheta)
(/ 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))
(* (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))))
(/ 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 (/ 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))
(* (pow cosTheta 2) (- (pow alpha 2) 1))
(* (pow cosTheta 2) (- (+ (/ 1 (pow cosTheta 2)) (pow alpha 2)) 1))
(/ (- (pow alpha 3) 1) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))) (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1)))))))))) (pow cosTheta 2))
(/ (- (+ (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (+ (/ 1 (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))) (+ (/ (pow alpha 3) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (pow alpha 3) (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2)))))))))) (+ (/ 1 (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (+ (/ 1 (* (pow cosTheta 4) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 2))))))) (+ (/ (pow alpha 3) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (- (pow alpha 2) 1))))))) (/ (pow alpha 3) (* (pow cosTheta 6) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (* (- alpha 1) (pow (- (pow alpha 2) 1) 3))))))))))) (pow cosTheta 2))
(* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1)))))
(* (pow cosTheta 2) (+ (* 2 (* (PI) (* (log alpha) (- (pow alpha 2) 1)))) (* 2 (/ (* (PI) (log alpha)) (pow cosTheta 2)))))
-1
(- (pow alpha 2) 1)
(/ -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))))))))
(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))))))
(- (* 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 (* (PI) (* (log alpha) (- 1 (pow cosTheta 2)))))
(* (PI) (log alpha))
(- (* 1/2 (/ (pow alpha 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(/ 1/2 (log alpha))
(- (pow alpha 3) 1)
(+ 1 (* -1 (pow cosTheta 2)))
(+ 1 (+ (* -1 (pow cosTheta 2)) (* (pow alpha 2) (pow cosTheta 2))))
(- (* (pow alpha 2) (- (+ (* 1/2 (/ 1 (* (PI) (* (log alpha) (+ 1 (* -1 (pow cosTheta 2))))))) (* (pow alpha 2) (- (* -1 (* alpha (+ (* -1 (- (* 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))))))) (* 1/2 (/ (pow cosTheta 2) (* (PI) (* (log alpha) (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 (PI))
(- (/ (pow alpha 2) (PI)) (/ 1 (PI)))
(+ 1 (* -1 (pow alpha 2)))
(+ 1 (* (pow alpha 2) (- (* -1 alpha) 1)))
(+ 1 (* (pow alpha 2) (- (* alpha (- (pow alpha 2) 1)) 1)))
(* 2 (* (pow cosTheta 2) (* (PI) (+ (* -1 (log alpha)) (/ (log alpha) (pow cosTheta 2))))))
(+ (* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log alpha))))) (* 2 (* (pow cosTheta 2) (* (PI) (+ (* -1 (log alpha)) (/ (log alpha) (pow cosTheta 2)))))))
(* (pow alpha 2) (- 1 (/ 1 (pow alpha 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))))))
(* -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)))))
(- (* 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 (* (PI) (* (log (/ 1 alpha)) (- 1 (pow cosTheta 2)))))
(/ 1/2 (* (PI) (log (/ 1 alpha))))
(* -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)))))))
(/ -1/2 (log (/ 1 alpha)))
(pow alpha 3)
(* (pow alpha 3) (- 1 (/ 1 (pow alpha 3))))
(* (pow alpha 2) (pow cosTheta 2))
(* (pow alpha 2) (+ (* -1 (/ (pow cosTheta 2) (pow alpha 2))) (+ (/ 1 (pow alpha 2)) (pow cosTheta 2))))
(- (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (+ (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha)))))) (* 1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow cosTheta 4) (* (PI) (log (/ 1 alpha)))))))) (pow alpha 5))) (/ 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 (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))))))
(* -2 (* (PI) (log (/ 1 alpha))))
(/ (pow alpha 2) (PI))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(pow alpha 5)
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (log (/ 1 alpha)) (* -1 (/ (log (/ 1 alpha)) (pow cosTheta 2)))))) (pow alpha 2)))))
(* -1 (/ (log (/ 1 alpha)) cosTheta))
(/ -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))))))
(* -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)))))
(/ 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 (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))))
(/ -1/2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* 1/2 (/ (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(/ 1/2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(* -2 (* (PI) (log (/ -1 alpha))))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (* -1 (+ (log -1) (* -1 (log (/ -1 alpha))))) (+ (* -1 (/ (log (/ -1 alpha)) (pow cosTheta 2))) (/ (log -1) (pow cosTheta 2)))))) (pow alpha 2)))))
(/ (+ (log -1) (* -1 (log (/ -1 alpha)))) cosTheta)

Outputs
(/ (- (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 (fma.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(- (+ (* (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)))))
(fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.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)))))
(fma.f32 (-.f32 (.f32 (fma.f32 (neg.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 4 binary32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(* (PI) (log (pow alpha 2)))
(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
(+ (* (PI) (log (pow alpha 2))) (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))
(fma.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))
(* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha))))
(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
(+ (* -1/2 (/ (* (pow cosTheta 2) (pow (- (pow alpha 2) 1) 2)) (* (PI) (log alpha)))) (* 1/2 (/ (- (pow alpha 2) 1) (* (PI) (log alpha)))))
(/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (.f32 cosTheta cosTheta) (.f32 #s(literal 1/2 binary32) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (PI.f32) (log.f32 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)))))))
(fma.f32 (/.f32 (fma.f32 (.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 #s(literal -1/2 binary32) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)))) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
(+ (* 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)))))))))
(fma.f32 (fma.f32 (/.f32 (fma.f32 #s(literal 1/2 binary32) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (.f32 (.f32 #s(literal -1/2 binary32) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 4 binary32))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 alpha))) (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)))) (.f32 cosTheta cosTheta) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
(/ -1/2 (* (PI) (log alpha)))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(- (* -1/2 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))))
(- (* (pow cosTheta 2) (- (* -1/2 (/ (pow cosTheta 2) (* (PI) (log alpha)))) (* 1/2 (/ 1 (* (PI) (log alpha)))))) (* 1/2 (/ 1 (* (PI) (log alpha)))))
(fma.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 cosTheta cosTheta) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 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)))))
(fma.f32 (fma.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 cosTheta cosTheta) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha)))) (.f32 cosTheta cosTheta) (/.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (log.f32 alpha))))
1
#s(literal 1 binary32)
(+ 1 (* (pow cosTheta 2) (- (pow alpha 2) 1)))
(fma.f32 (.f32 cosTheta cosTheta) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 1 binary32))
(/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))
(.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32)))))
(+ (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(/.f32 (fma.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32))))
(+ (* (pow cosTheta 2) (- (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(fma.f32 (-.f32 (.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))))) (.f32 (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32)))))) (.f32 cosTheta cosTheta) (.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))))))
(+ (* (pow cosTheta 2) (- (* (pow cosTheta 2) (- (* -1 (/ (* (pow cosTheta 2) (* (pow (- (pow alpha 2) 1) 4) (- (pow alpha 3) 1))) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))) (* -1 (/ (* (pow (- (pow alpha 2) 1) 3) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1)))))))) (/ (* (pow (- (pow alpha 2) 1) 2) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))) (/ (* (- (pow alpha 2) 1) (- (pow alpha 3) 1)) (* (PI) (* (log (pow alpha 2)) (* (+ 1 (+ alpha (pow alpha 2))) (- alpha 1))))))
(fma.f32 (fma.f32 (fma.f32 (neg.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32))) (.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 4 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32)))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 alpha #s(literal 1 binary32)))) (.f32 (/.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 3 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32)))))) (.f32 cosTheta cosTheta) (.f32 (neg.f32 (/.f32 (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32)) (PI.f32))) (/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32)))) (-.f32 alpha #s(literal 1 binary32))))) (.f32 cosTheta cosTheta) (.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))))))
(* 2 (* (PI) (log alpha)))
(.f32 (.f32 (PI.f32) (log.f32 alpha)) #s(literal 2 binary32))
(+ (* 2 (* (PI) (log alpha))) (* 2 (* (pow cosTheta 2) (* (PI) (* (log alpha) (- (pow alpha 2) 1))))))
(.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha))))
(/ (log alpha) cosTheta)
(/.f32 (log.f32 alpha) cosTheta)
(/ 1 (* (pow cosTheta 2) (* (PI) (log (pow alpha 2)))))
(/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(/ (- (/ 1 (* (PI) (log (pow alpha 2)))) (/ 1 (* (pow cosTheta 2) (* (PI) (* (log (pow alpha 2)) (- (pow alpha 2) 1)))))) (pow cosTheta 2))
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(-.f32 (fma.f32 (/.f32 (.f32 #s(literal 0 binary32) (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (.f32 (neg.f32 (log.f32 alpha)) (PI.f32))))) (pow.f32 alpha #s(literal 5 binary32))) #s(literal -1 binary32) (+.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (neg.f32 (log.f32 alpha)))) (.f32 (/.f32 (/.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)) #s(literal -1/2 binary32)))) (fma.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (pow.f32 cosTheta #s(literal 4 binary32)))) (.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (neg.f32 (log.f32 alpha)))))
(* -2 (* (PI) (log (/ 1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (neg.f32 (log.f32 alpha)))
(/ (pow alpha 2) (PI))
(/.f32 (*.f32 alpha alpha) (PI.f32))
(* (pow alpha 2) (- (/ 1 (PI)) (/ 1 (* (pow alpha 2) (PI)))))
(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha))
(pow alpha 5)
(pow.f32 alpha #s(literal 5 binary32))
(* (pow alpha 5) (- 1 (/ 1 (pow alpha 2))))
(.f32 (pow.f32 alpha #s(literal 5 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))))
(* (pow alpha 5) (+ 1 (* -1 (/ (+ 1 (/ 1 alpha)) (pow alpha 2)))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 5) (- (+ 1 (/ 1 (pow alpha 5))) (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3)))))
(*.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ 1 alpha))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (log (/ 1 alpha)) (* -1 (/ (log (/ 1 alpha)) (pow cosTheta 2)))))) (pow alpha 2)))))
(.f32 (.f32 #s(literal -2 binary32) (-.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (neg.f32 (log.f32 alpha))) (/.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (-.f32 (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta) (log.f32 alpha))) (.f32 alpha alpha)))) (.f32 alpha alpha))
(* -1 (/ (log (/ 1 alpha)) cosTheta))
(/.f32 (log.f32 alpha) cosTheta)
(/ -1/2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(- (/ 1/2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha)))))) (+ (* -1/2 (/ (+ 1 (* -1 (pow cosTheta 2))) (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))))
(-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) 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 (fma.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 alpha alpha)) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) 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 (fma.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (pow.f32 alpha #s(literal 6 binary32)) (pow.f32 cosTheta #s(literal 4 binary32)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) alpha) alpha) (fma.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (/.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal -1/2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 (.f32 (pow.f32 alpha #s(literal 4 binary32)) cosTheta) cosTheta)) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(* -2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 2) (+ (* -2 (* (pow cosTheta 2) (* (PI) (log (/ -1 alpha))))) (* -2 (/ (* (PI) (* (log (/ -1 alpha)) (+ 1 (* -1 (pow cosTheta 2))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)) (/.f32 (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (*.f32 alpha alpha))))
(/ 1/2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(- (* 1/2 (/ 1 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (pow cosTheta 4) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(-.f32 (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) 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)))))))))
(-.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (*.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) 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)))))))))
(-.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) (pow.f32 alpha #s(literal 6 binary32))) (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 8 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (pow.f32 alpha #s(literal 4 binary32))) (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (/.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (.f32 (.f32 (pow.f32 cosTheta #s(literal 4 binary32)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))))
(/ -1/2 (* (PI) (* (+ (log -1) (* -1 (log (/ -1 alpha)))) (- 1 (pow cosTheta 2)))))
(/.f32 (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(/ -1/2 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))
(/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))
(*.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (PI.f32))
(* 1/2 (/ (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha)))))))
(/.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (.f32 alpha alpha)) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* (pow alpha 2) (- (* 1/2 (/ 1 (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 1/2 (/ 1 (* (pow alpha 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))))
(.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))) (.f32 alpha alpha))
(/ 1/2 (+ (log -1) (* -1 (log (/ -1 alpha)))))
(/.f32 #s(literal 1/2 binary32) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))))
(* -1 (* (pow alpha 3) (- (/ 1 (pow alpha 3)) 1)))
(*.f32 (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 3 binary32))) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 3 binary32)))
(* 2 (* (pow alpha 2) (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (PI) (* (+ 1 (* -1 (pow cosTheta 2))) (+ (log -1) (* -1 (log (/ -1 alpha)))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (/.f32 (.f32 (.f32 (PI.f32) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))) (*.f32 alpha alpha))))
(* -2 (* (PI) (log (/ -1 alpha))))
(.f32 (.f32 #s(literal -2 binary32) (PI.f32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha)))
(* -1 (* (pow alpha 5) (- (/ 1 (pow alpha 2)) 1)))
(.f32 (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32))) (pow.f32 alpha #s(literal 5 binary32)))
(* -1 (* (pow alpha 5) (- (+ (/ 1 (pow alpha 2)) (/ 1 (pow alpha 3))) 1)))
(*.f32 (neg.f32 (pow.f32 alpha #s(literal 5 binary32))) (-.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha) #s(literal 1 binary32)))
(* -1 (* (pow alpha 5) (- (+ (* -1 (/ (- (/ 1 (pow alpha 2)) 1) (pow alpha 3))) (/ 1 (pow alpha 2))) 1)))
(.f32 (neg.f32 (pow.f32 alpha #s(literal 5 binary32))) (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) #s(literal 1 binary32)) (pow.f32 alpha #s(literal 3 binary32))) #s(literal -1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha)) #s(literal 1 binary32))))
(* (pow alpha 2) (+ (* 2 (* (pow cosTheta 2) (* (PI) (+ (log -1) (* -1 (log (/ -1 alpha))))))) (* 2 (/ (* (pow cosTheta 2) (* (PI) (+ (* -1 (+ (log -1) (* -1 (log (/ -1 alpha))))) (+ (* -1 (/ (log (/ -1 alpha)) (pow cosTheta 2))) (/ (log -1) (pow cosTheta 2)))))) (pow alpha 2)))))
(.f32 (.f32 (.f32 alpha alpha) #s(literal 2 binary32)) (.f32 (.f32 cosTheta cosTheta) (fma.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (PI.f32) (/.f32 (.f32 (fma.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) #s(literal -1 binary32) (/.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 alpha alpha)))))
(/ (+ (log -1) (* -1 (log (/ -1 alpha)))) cosTheta)
(/.f32 (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) alpha))) cosTheta)

rewrite161.0ms (2.1%)

Memory

-9.5MiB live, 223.9MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	444
0	119	396
1	439	366
2	3599	366
0	8297	366

Stop Event

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

Counts

23 → 483

Calls

Call 1

Inputs
(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(*.f32 alpha alpha)
(.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32)))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))
(*.f32 (PI.f32) (log.f32 alpha))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
(.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)))
(/.f32 #s(literal 1/2 binary32) (log.f32 alpha))
(*.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))
(+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
#s(approx (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta)))))
(.f32 (PI.f32) #s(approx (log ( alpha alpha)) (*.f32 (log.f32 alpha) #s(literal 2 binary32))))
(/.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))
#s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32))
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))
#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
(/.f32 (log.f32 alpha) cosTheta)

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

eval131.0ms (1.7%)

Memory: 27.8MiB live, 256.2MiB allocated; 44ms collecting garbage
Compiler: Compiled 47 093 to 3 298 computations (93% saved)

prune120.0ms (1.6%)

Memory

-15.6MiB live, 200.2MiB allocated; 78ms collecting garbage

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	858	21	879
Fresh	15	9	24
Picked	4	1	5
Done	0	2	2
Total	877	33	910

Accuracy

100.0%

Counts

910 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(approx (log ( alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha)))))
	98.6%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
✓	-0.0%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
	98.4%	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) #s(approx (log (* alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
	97.7%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
	66.0%	(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
	97.5%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
	97.1%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
	98.3%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.2%	(.f32 (/.f32 (+.f32 #s(literal 1 binary32) alpha) (PI.f32)) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) #s(approx (log ( alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha))))))
	98.3%	(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(approx (log (* alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha))))))
✓	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) #s(literal 1/2 binary32)) (log.f32 alpha)))
	94.9%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32)))
	95.0%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
	94.5%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))))
	94.2%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (cbrt.f32 (PI.f32)))))
	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 #s(literal 1 binary32) alpha))) (PI.f32))))
	94.2%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (+.f32 #s(literal 1 binary32) alpha)) (PI.f32))))
	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (.f32 (PI.f32) #s(literal 1 binary32))) (*.f32 (PI.f32) (PI.f32)))))
	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (PI.f32))))
	94.3%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 #s(approx (- ( alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)) (PI.f32))))
	94.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
	94.3%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) #s(approx (/ (- ( alpha alpha) 1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha)))))
	94.9%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha))))
	67.4%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) cosTheta) cosTheta #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
	66.8%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (PI.f32))))
	66.7%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))))
✓	66.7%	#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
	68.0%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Compiler

Compiled 4 532 to 1 301 computations (71.3% saved)

regimes111.0ms (1.5%)

Memory

26.3MiB live, 125.7MiB allocated; 46ms collecting garbage

Counts

74 → 1

Calls

Call 1

Inputs
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ 0 0)) (*.f32 (NAN.f32) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))) (/.f32 #s(literal 0 binary32) #s(literal 0 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 #s(literal -1/2 binary32) (*.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (/.f32 #s(literal -1/2 binary32) (log.f32 alpha)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (/ (/ -1/2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (/.f32 (fma.f32 (.f32 #s(literal -1/2 binary32) cosTheta) cosTheta #s(literal -1/2 binary32)) (.f32 (PI.f32) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (.f32 #s(literal 1/2 binary32) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) #s(literal 2 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 #s(literal 1/2 binary32) (PI.f32)) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (/.f32 #s(literal 1/2 binary32) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (fma.f32 alpha alpha #s(literal -1 binary32))) (PI.f32)))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (*.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) #s(literal 1/2 binary32)) (log.f32 alpha)))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (+ (* alpha alpha) -1) (* cosTheta cosTheta)) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log (* alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(approx (log ( alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (-.f32 (.f32 (.f32 alpha alpha) (PI.f32)) (.f32 (PI.f32) #s(literal 1 binary32))) (*.f32 (PI.f32) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) #s(approx (log ( alpha alpha)) (.f32 (log.f32 alpha) #s(literal 2 binary32)))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (*.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) (PI.f32)) #s(approx (log (* alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha))))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) (+.f32 #s(literal 1 binary32) alpha)) (PI.f32))))
(/.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 (.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 alpha)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 #s(approx (- ( alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #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) alpha) (PI.f32)) (/.f32 (-.f32 alpha #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)) #s(approx (log ( alpha alpha)) (*.f32 #s(literal 2 binary32) (log.f32 alpha))))))
(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) #s(approx (log (* alpha alpha)) (.f32 #s(literal 2 binary32) (log.f32 alpha)))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32)))
(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32) (.f32 (-.f32 alpha #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))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) #s(approx (/ (- ( alpha alpha) 1) (PI)) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 alpha alpha)) (PI.f32))) (*.f32 alpha alpha)))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 #s(literal 1 binary32) alpha))) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ 1 (* alpha alpha))) alpha) (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) 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(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) #s(literal 1 binary32)) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (.f32 cosTheta cosTheta) #s(literal 1 binary32))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (-.f32 #s(literal 1 binary32) (.f32 alpha alpha))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (neg.f32 alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (fma.f32 (-.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) alpha) #s(literal 1 binary32)) (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))) (*.f32 (log.f32 alpha) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.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)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (.f32 (log.f32 alpha) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32))) (.f32 (log.f32 alpha) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 cosTheta cosTheta) #s(literal 2 binary32)) (.f32 (PI.f32) (fma.f32 (log.f32 alpha) (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (/.f32 (log.f32 alpha) cosTheta) cosTheta))))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) alpha) alpha)) alpha) alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.f32 #s(literal 1 binary32) alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #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 (-.f32 (pow.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 2 binary32)) #s(literal 1 binary32)) (-.f32 (.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta) #s(literal 1 binary32)))))
(/.f32 (-.f32 (/.f32 (pow.f32 alpha #s(literal 4 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 alpha alpha #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 6 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) alpha) (fma.f32 alpha alpha (+.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 alpha alpha) #s(literal 1 binary32)) #s(approx ( (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (.f32 alpha alpha) #s(literal -2 binary32)) (fma.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta) (/.f32 (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (*.f32 alpha alpha))))))
(/.f32 (/.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (+.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (+.f32 #s(literal 1 binary32) alpha) (-.f32 (fma.f32 alpha alpha #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 (fma.f32 alpha alpha #s(literal -1 binary32)) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (/.f32 (.f32 cosTheta cosTheta) (PI.f32)) (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32)))) (log.f32 alpha))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 #s(approx (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal 5 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) alpha) #s(literal 1 binary32)) alpha) alpha)) (pow.f32 alpha #s(literal 5 binary32)))) (.f32 (-.f32 alpha #s(literal 1 binary32)) (fma.f32 alpha alpha (+.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))))
#s(approx (/ (- (* alpha alpha) 1) (* (+ (* (* (log alpha) (pow (cbrt (PI)) 2)) (cbrt (PI))) (* (log alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (*.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (cbrt.f32 (PI.f32)))))
(/.f32 (/.f32 (-.f32 (+.f32 (pow.f32 alpha #s(literal 4 binary32)) (pow.f32 alpha #s(literal 6 binary32))) (fma.f32 alpha alpha #s(literal 1 binary32))) (pow.f32 (fma.f32 alpha alpha #s(literal 1 binary32)) #s(literal 2 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))))
#s(approx (/ (/ (* (+ (* alpha alpha) -1) (- (pow alpha 3) 1)) (* (- alpha 1) (+ (* alpha alpha) (+ 1 alpha)))) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 (fma.f32 (.f32 (.f32 (neg.f32 cosTheta) cosTheta) (pow.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(literal 2 binary32))) (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 (pow.f32 alpha #s(literal 3 binary32)) #s(literal 1 binary32)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)))) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 (fma.f32 alpha alpha alpha) #s(literal 1 binary32))) (*.f32 (-.f32 alpha #s(literal 1 binary32)) (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (log.f32 (pow.f32 (.f32 alpha alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))))) (+.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 (fma.f32 (.f32 (log.f32 alpha) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)) (.f32 (log.f32 alpha) (PI.f32))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 (-.f32 (.f32 (/.f32 (.f32 cosTheta cosTheta) (log.f32 (.f32 alpha alpha))) (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) (PI.f32))) (/.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 2 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (.f32 cosTheta cosTheta) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))

Outputs

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

Calls

4 calls:

54.0ms	alpha
19.0ms	(/.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)
17.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.6%	1	`(*.f32 alpha 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	`cosTheta`
98.6%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes31.0ms (0.4%)

Memory

-4.8MiB live, 40.9MiB allocated; 4ms collecting garbage

Counts

25 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

9.0ms	(/.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))))
7.0ms	(*.f32 alpha alpha)
7.0ms	alpha
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
98.6%	1	`cosTheta`
98.6%	1	`(*.f32 alpha 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	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes30.0ms (0.4%)

Memory

8.9MiB live, 54.8MiB allocated; 4ms collecting garbage

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

9.0ms	(/.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))))
6.0ms	alpha
6.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.5%	1	`cosTheta`
97.5%	1	`(*.f32 alpha alpha)`
97.5%	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))))`
97.5%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes38.0ms (0.5%)

Memory

4.0MiB live, 52.5MiB allocated; 17ms collecting garbage

Counts

22 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

18.0ms	cosTheta
6.0ms	(/.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))))
6.0ms	(*.f32 alpha alpha)
6.0ms	alpha

Results

Accuracy	Segments	Branch
97.4%	1	`(*.f32 alpha alpha)`
97.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
97.4%	1	`cosTheta`
97.4%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes28.0ms (0.4%)

Memory

8.0MiB live, 54.6MiB allocated; 5ms collecting garbage

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

9.0ms	alpha
6.0ms	(/.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))))
6.0ms	(*.f32 alpha alpha)
6.0ms	cosTheta

Results

Accuracy	Segments	Branch
95.0%	1	`cosTheta`
95.0%	1	`(*.f32 alpha alpha)`
95.0%	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))))`
95.0%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes32.0ms (0.4%)

Memory

-26.6MiB live, 19.9MiB allocated; 4ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	alpha
2.0ms	cosTheta
2.0ms	(/.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))))
2.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
67.4%	1	`(*.f32 alpha alpha)`
67.4%	1	`(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))`
67.4%	1	`cosTheta`
67.4%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes9.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes27.0ms (0.4%)

Memory

-30.0MiB live, 17.2MiB allocated; 2ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

21.0ms	cosTheta
2.0ms	(/.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))))
2.0ms	(*.f32 alpha alpha)
2.0ms	alpha

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes6.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

simplify98.0ms (1.3%)

Memory

-54.7MiB live, 30.6MiB allocated; 130ms collecting garbage

Algorithm

1×	egg-herbie

Stop Event

1×	iter limit
1×	unsound

Calls

Call 1

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

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

derivations931.0ms (12.2%)

Memory

18.8MiB live, 768.5MiB allocated; 118ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1450
1	572	1398
2	2417	1236
0	8614	1182
0	485	3852
1	1581	3637
2	7479	3381
0	8681	3320
0	75	444
0	119	396
1	439	366
2	3599	366
0	8297	366
0	640	5538
1	2031	5157
0	8959	5042
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55

Stop Event

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

Compiler

Compiled 363 to 91 computations (74.9% saved)

preprocess124.0ms (1.6%)

Memory

33.1MiB live, 122.9MiB allocated; 7ms collecting garbage

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 878 to 276 computations (68.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze59.0ms (0.8%)

sample2.3s (30.4%)

explain192.0ms (2.5%)

preprocess134.0ms (1.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify120.0ms (1.6%)

localize69.0ms (0.9%)

series72.0ms (0.9%)

simplify199.0ms (2.6%)

rewrite211.0ms (2.8%)

eval115.0ms (1.5%)

prune35.0ms (0.5%)

simplify9.0ms (0.1%)

localize211.0ms (2.8%)

series313.0ms (4.1%)

simplify237.0ms (3.1%)

rewrite49.0ms (0.6%)

eval22.0ms (0.3%)

prune31.0ms (0.4%)

simplify9.0ms (0.1%)

localize251.0ms (3.3%)

series98.0ms (1.3%)

simplify263.0ms (3.4%)

rewrite17.0ms (0.2%)

eval21.0ms (0.3%)

prune28.0ms (0.4%)

simplify144.0ms (1.9%)

localize187.0ms (2.4%)

series166.0ms (2.2%)

simplify183.0ms (2.4%)

rewrite161.0ms (2.1%)

eval131.0ms (1.7%)

prune120.0ms (1.6%)

regimes111.0ms (1.5%)

regimes31.0ms (0.4%)

regimes30.0ms (0.4%)

regimes38.0ms (0.5%)

regimes28.0ms (0.4%)

regimes32.0ms (0.4%)

regimes9.0ms (0.1%)

regimes27.0ms (0.4%)

regimes6.0ms (0.1%)

simplify98.0ms (1.3%)

derivations931.0ms (12.2%)

preprocess124.0ms (1.6%)

end0.0ms (0%)

Profiling