Metrics for GTR1 distribution

start0.0ms (0%)

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

analyze84.0ms (1.2%)

Memory

-27.6MiB live, 68.8MiB allocated; 66ms 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)

sample1.7s (24.7%)

Memory

35.7MiB live, 1 662.4MiB allocated; 514ms collecting garbage

Samples

1.3s

8 256×

valid

Precisions

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

ival-mult: 310.0ms (30.1% of total)

const: 294.0ms (28.6% of total)

ival-log: 93.0ms (9% of total)

ival-<=: 90.0ms (8.7% of total)

ival-sub: 69.0ms (6.7% of total)

ival-div: 65.0ms (6.3% of total)

ival-add: 39.0ms (3.8% of total)

ival-pi: 31.0ms (3% of total)

ival-and: 23.0ms (2.2% of total)

exact: 10.0ms (1% of total)

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

adjust: 2.0ms (0.2% of total)

Bogosity

explain193.0ms (2.8%)

Memory

-38.8MiB live, 256.5MiB allocated; 37ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	2	254

Precision?

0.0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0.0

Recall?

0/0

Samples

55.0ms

512×

valid

Compiler

Compiled 210 to 43 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 16.0ms (39.9% of total)

ival-sub: 7.0ms (17.5% of total)

ival-div: 6.0ms (15% of total)

ival-log: 5.0ms (12.5% of total)

ival-add: 3.0ms (7.5% of total)

ival-pi: 2.0ms (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)

preprocess135.0ms (2%)

Memory

10.6MiB live, 151.3MiB allocated; 40ms 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
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))

Status

Accuracy

Program

▶

98.6%

(/.f32 (-.f32 (*.f32 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)

simplify104.0ms (1.5%)

Memory

6.6MiB live, 93.7MiB allocated; 20ms 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

localize57.0ms (0.8%)

Memory

11.0MiB live, 54.1MiB allocated; 9ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta)
accuracy	0.21875	(.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) cosTheta)
accuracy	0.3326950195368841	(/.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	0.34375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Samples

48.0ms

256×

valid

Compiler

Compiled 93 to 15 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 8.0ms (49.5% of total)

ival-log: 3.0ms (18.6% of total)

ival-div: 2.0ms (12.4% of total)

ival-pi: 1.0ms (6.2% of total)

ival-add: 1.0ms (6.2% of total)

ival-sub: 1.0ms (6.2% 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)

series110.0ms (1.6%)

Memory

8.0MiB live, 117.5MiB allocated; 43ms 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
80.0ms	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))
14.0ms	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))

simplify145.0ms (2.1%)

Memory

-5.6MiB live, 142.2MiB allocated; 16ms 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)))

rewrite171.0ms (2.5%)

Memory

-16.2MiB live, 218.6MiB allocated; 33ms 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))

eval73.0ms (1.1%)

Memory: 11.0MiB live, 100.9MiB allocated; 7ms collecting garbage
Compiler: Compiled 19 163 to 2 092 computations (89.1% saved)

prune47.0ms (0.7%)

Memory

-21.1MiB live, 76.9MiB allocated; 13ms 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

99.9%

Counts

508 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
▶	-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))))
	98.2%	(/.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))))
	97.9%	(/.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))))
	98.0%	(/.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))))
	97.6%	(/.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))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.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))))
	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))))
	97.6%	(/.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))))
	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) 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 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
	97.4%	(/.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)))))
	95.0%	(/.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))))
▶	98.7%	(/.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))))
	98.1%	(/.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))))
▶	97.8%	(/.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))))
	65.6%	(/.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))))
▶	97.4%	#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)))))
	96.5%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.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))))
	94.8%	#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))))
	65.6%	#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 1 578 to 932 computations (40.9% saved)

simplify9.0ms (0.1%)

Memory

23.0MiB live, 23.0MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	667
0	108	667

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

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

localize200.0ms (2.9%)

Memory

-20.2MiB live, 266.4MiB allocated; 42ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(.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)))
accuracy	0.0	(log.f32 alpha)
accuracy	0.0	#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)))))
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 (fma.f32 alpha alpha #s(literal -1 binary32)))
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 (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)

Samples

156.0ms

256×

invalid

Compiler

Compiled 620 to 54 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-mult: 43.0ms (38.5% of total)

ival-log: 31.0ms (27.8% of total)

ival-div: 18.0ms (16.1% of total)

ival-add: 6.0ms (5.4% of total)

ival-pow: 5.0ms (4.5% of total)

ival-sub: 4.0ms (3.6% of total)

ival-pow2: 3.0ms (2.7% of total)

ival-pi: 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)

series168.0ms (2.4%)

Memory

38.9MiB live, 221.2MiB allocated; 30ms collecting garbage

Counts

23 → 132

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
52.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha 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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* 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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (log alpha))
37.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha 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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* 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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (log alpha))
34.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha 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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* 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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (log alpha))
20.0ms	cosTheta	@	0	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha 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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* 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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (log alpha))
12.0ms	cosTheta	@	-inf	((/ (- (* alpha alpha) 1) (* (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* alpha alpha) (* (log (pow (* alpha 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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* 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) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha)) (PI) (log (pow (* alpha alpha) (PI))) (* cosTheta (+ (* alpha alpha) -1)) (log (* alpha alpha)) (log alpha))

simplify170.0ms (2.5%)

Memory

32.0MiB live, 207.1MiB allocated; 50ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	535	4139
1	1642	3890
2	7115	3890
0	8667	3778

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 131

Calls

Call 1

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

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

rewrite48.0ms (0.7%)

Memory

-14.7MiB live, 42.0MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	397
0	108	397

Stop Event

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

Counts

23 → 25

Calls

Call 1

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

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

eval35.0ms (0.5%)

Memory: 6.6MiB live, 51.9MiB allocated; 2ms collecting garbage
Compiler: Compiled 11 406 to 916 computations (92% saved)

prune31.0ms (0.4%)

Memory

-20.0MiB live, 68.9MiB allocated; 8ms collecting garbage

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	187	18	205
Fresh	8	11	19
Picked	3	2	5
Done	0	0	0
Total	198	31	229

Accuracy

100.0%

Counts

229 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
	98.4%	(/.f32 (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))))
▶	-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))))
	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))))
	98.2%	(/.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))))
	97.9%	(/.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))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.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))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
▶	97.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.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 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
✓	98.7%	(/.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))))
▶	55.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
	95.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (fma.f32 (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta) (.f32 (log.f32 alpha) (PI.f32)) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha))) #s(literal 2 binary32))))
	97.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha 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)))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (*.f32 cosTheta cosTheta))))))
	95.2%	(/.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)))))
	98.1%	(/.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))))
▶	98.0%	(/.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 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	96.7%	(/.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))))
	98.4%	(/.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))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	65.7%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	94.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(approx (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	94.8%	#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))))
	65.6%	#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))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	65.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))

Compiler

Compiled 2 502 to 1 445 computations (42.2% saved)

simplify8.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	547
0	98	547

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

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

localize154.0ms (2.2%)

Memory

-35.1MiB live, 106.4MiB allocated; 93ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Samples

108.0ms

256×

invalid

Compiler

Compiled 491 to 44 computations (91% saved)

Precisions

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

ival-mult: 65.0ms (72.2% of total)

ival-div: 9.0ms (10% of total)

ival-add: 6.0ms (6.7% of total)

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

ival-log: 3.0ms (3.3% of total)

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

ival-neg: 1.0ms (1.1% 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)

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

series76.0ms (1.1%)

Memory

-12.4MiB live, 128.2MiB allocated; 23ms collecting garbage

Counts

22 → 108

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	cosTheta	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (/ (+ (* 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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* (* (- 1 (/ (/ 1 alpha) alpha)) alpha) alpha) (* (- 1 (/ (/ 1 alpha) alpha)) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha cosTheta) cosTheta)) (NAN) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta))
16.0ms	alpha	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (/ (+ (* 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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* (* (- 1 (/ (/ 1 alpha) alpha)) alpha) alpha) (* (- 1 (/ (/ 1 alpha) alpha)) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha cosTheta) cosTheta)) (NAN) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta))
14.0ms	alpha	@	0	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (/ (+ (* 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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* (* (- 1 (/ (/ 1 alpha) alpha)) alpha) alpha) (* (- 1 (/ (/ 1 alpha) alpha)) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha cosTheta) cosTheta)) (NAN) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta))
11.0ms	alpha	@	inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (/ (+ (* 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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* (* (- 1 (/ (/ 1 alpha) alpha)) alpha) alpha) (* (- 1 (/ (/ 1 alpha) alpha)) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha cosTheta) cosTheta)) (NAN) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta))
8.0ms	cosTheta	@	-inf	((/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (- (* alpha alpha) 1) (* alpha alpha) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (/ (+ (* 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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (- (* alpha alpha) 1) (* (* (- 1 (/ (/ 1 alpha) alpha)) alpha) alpha) (* (- 1 (/ (/ 1 alpha) alpha)) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (PI) (log (* alpha alpha)) (* cosTheta (+ (* alpha cosTheta) cosTheta)) (NAN) (* cosTheta (+ (* alpha alpha) -1)) (neg cosTheta))

simplify162.0ms (2.4%)

Memory

15.2MiB live, 244.3MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	608	4827
1	2009	4366
0	9340	4207

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 107

Calls

Call 1

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

rewrite17.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	326
0	98	326

Stop Event

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

Counts

22 → 23

Calls

Call 1

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

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

eval21.0ms (0.3%)

Memory: -5.8MiB live, 38.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 9 618 to 854 computations (91.1% saved)

prune36.0ms (0.5%)

Memory

11.1MiB live, 56.3MiB allocated; 3ms collecting garbage

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	164	12	176
Fresh	6	18	24
Picked	4	1	5
Done	0	2	2
Total	174	33	207

Accuracy

100.0%

Counts

207 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	-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))))
	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))))
	98.2%	(/.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))))
	97.9%	(/.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))))
	98.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (fma.f32 (.f32 (log.f32 alpha) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.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))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	96.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #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 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
✓	98.7%	(/.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))))
▶	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
▶	95.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 #s(literal 2 binary32) (fma.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 alpha) (.f32 (.f32 (.f32 #s(literal 0 binary32) (log.f32 alpha)) (PI.f32)) alpha)))))
▶	54.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
▶	97.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha 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)))))
	98.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 #s(literal -2 binary32) (.f32 alpha alpha)) (fma.f32 (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))) (/.f32 (PI.f32) (.f32 alpha alpha)) (.f32 (neg.f32 (.f32 (log.f32 alpha) (PI.f32))) (*.f32 cosTheta cosTheta))))))
	95.2%	(/.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)))))
	98.1%	(/.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))))
	98.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
	97.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	96.8%	(/.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 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
▶	96.7%	(/.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))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	65.7%	(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
	94.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	65.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	94.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	96.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (fma.f32 #s(approx (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (/.f32 #s(literal 1/2 binary32) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 alpha alpha) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	65.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))))
	97.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))

Compiler

Compiled 2 674 to 1 572 computations (41.2% saved)

simplify201.0ms (2.9%)

Memory

-31.6MiB live, 149.5MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))))
cost-diff	1	(+.f32 #s(literal 1 binary32) (.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta))
cost-diff	0	#s(approx (* (log (pow (* alpha 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))))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha 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)))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	0	(*.f32 alpha alpha)
cost-diff	0	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
cost-diff	1	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
cost-diff	5	(fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	713
0	107	689
1	261	665
2	890	665
3	4136	665
0	8515	651

Stop Event

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

Calls

Call 1

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

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

localize203.0ms (3%)

Memory

19.5MiB live, 311.7MiB allocated; 61ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.17644501953688402	(/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))
accuracy	0.3326950195368841	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
accuracy	11.341126473260118	#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy	13.892919742645025	(.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))
accuracy	0.3326950195368841	(/.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))))
accuracy	0.34375	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
accuracy	0.37109375	(.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 alpha alpha))) alpha) alpha)
accuracy	11.341126473260118	#s(approx (- (* alpha alpha) 1) #s(literal -1 binary32))
accuracy	0.07259750976844201	(-.f32 (*.f32 alpha alpha) #s(literal 1 binary32))
accuracy	0.3326950195368841	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha 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)))))
accuracy	0.3515625	(.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha)))
accuracy	0.423794534292676	#s(approx (* (log (pow (* alpha 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))))
accuracy	0.11232377930532605	(log.f32 (*.f32 alpha alpha))
accuracy	0.3326950195368841	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
accuracy	0.34375	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))
accuracy	1.1745935334756155	#s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))
accuracy	0.203125	(.f32 (.f32 (*.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32)))
accuracy	0.27962875976844204	(.f32 (.f32 cosTheta cosTheta) (PI.f32))
accuracy	0.3326950195368841	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
accuracy	0.34375	(.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))

Samples

155.0ms

256×

valid

Compiler

Compiled 542 to 55 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

ival-mult: 63.0ms (61.4% of total)

ival-add: 11.0ms (10.7% of total)

ival-div: 10.0ms (9.8% of total)

ival-log: 7.0ms (6.8% of total)

ival-sub: 5.0ms (4.9% of total)

ival-pow: 5.0ms (4.9% of total)

ival-pi: 1.0ms (1% 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)

series155.0ms (2.3%)

Memory

-8.7MiB live, 315.1MiB allocated; 54ms collecting garbage

Counts

23 → 114

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta	@	0	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (- (* alpha alpha) 1) (* (PI) (log (* alpha alpha))) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))
22.0ms	alpha	@	-inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (- (* alpha alpha) 1) (* (PI) (log (* alpha alpha))) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))
22.0ms	alpha	@	inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (- (* alpha alpha) 1) (* (PI) (log (* alpha alpha))) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))
21.0ms	alpha	@	0	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (- (* alpha alpha) 1) (* (PI) (log (* alpha alpha))) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))
20.0ms	cosTheta	@	-inf	((+ (* (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha))) (* (log (* alpha alpha)) (PI))) (- (* alpha alpha) 1) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* alpha alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 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))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (- (* alpha alpha) 1) (* (* (- 1 (/ 1 (* alpha alpha))) alpha) alpha) (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (* (log (* alpha alpha)) (PI)) (* (* cosTheta cosTheta) (PI)) (* (* (* cosTheta cosTheta) (PI)) (+ (* alpha alpha) -1)) (log (* alpha alpha)) (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (- (* alpha alpha) 1) (* (PI) (log (* alpha alpha))) (* (* (PI) (+ (* (log (* alpha alpha)) (- (* alpha alpha) 1)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))) (* cosTheta cosTheta)) (/ (log (* alpha alpha)) (* cosTheta cosTheta)))

simplify241.0ms (3.5%)

Memory

7.5MiB live, 293.2MiB allocated; 59ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	613	4823
1	2033	4375
0	8648	4205

Stop Event

1×	iter limit
1×	node limit

Counts

114 → 114

Calls

Call 1

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

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

rewrite155.0ms (2.3%)

Memory

32.9MiB live, 215.5MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	462
0	107	447
1	438	424
2	3497	424
0	8315	413

Stop Event

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

Counts

23 → 497

Calls

Call 1

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

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

eval136.0ms (2%)

Memory: -17.5MiB live, 218.6MiB allocated; 26ms collecting garbage
Compiler: Compiled 54 836 to 3 879 computations (92.9% saved)

prune64.0ms (0.9%)

Memory

7.0MiB live, 157.0MiB allocated; 15ms collecting garbage

Pruning

43 alts after pruning (40 fresh and 3 done)

	Pruned	Kept	Total
New	1 019	28	1 047
Fresh	13	12	25
Picked	4	1	5
Done	1	2	3
Total	1 037	43	1 080

Accuracy

100.0%

Counts

1 080 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
✓	-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))))
	94.9%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	98.4%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
	95.1%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	97.3%	(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)))))
	94.8%	(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	94.4%	(/.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	96.9%	(/.f32 (/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (pow.f32 alpha #s(literal -2 binary32))) alpha) alpha)) (PI.f32)) (.f32 (fma.f32 (.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (*.f32 alpha alpha))))
✓	98.6%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	96.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
	98.7%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (*.f32 (/.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 (pow.f32 alpha #s(literal 4 binary32))))))
	94.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)))))
	94.4%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
	94.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
✓	95.0%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	54.9%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (fma.f32 (.f32 (.f32 (.f32 #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) cosTheta) cosTheta) (PI.f32)) (log.f32 (.f32 alpha alpha)) (.f32 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (*.f32 cosTheta cosTheta)))))
	97.2%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (log.f32 alpha))))
	97.3%	(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
	94.7%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	97.1%	(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
	96.8%	(/.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 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	98.0%	(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha))) (.f32 alpha alpha)))))
	58.5%	(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #s(literal 1 binary32)) cosTheta) cosTheta))))
	94.4%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	54.5%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 alpha alpha))) alpha) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (PI.f32) (fma.f32 (log.f32 (.f32 alpha alpha)) #s(approx (- ( alpha alpha) 1) #s(literal -1 binary32)) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))) (*.f32 cosTheta cosTheta))))
	98.2%	(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (fma.f32 (.f32 (.f32 (.f32 cosTheta cosTheta) (PI.f32)) (fma.f32 alpha alpha #s(literal -1 binary32))) (log.f32 (.f32 alpha alpha)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
	64.2%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
	65.6%	(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)))))
	98.3%	(-.f32 (/.f32 (.f32 alpha alpha) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))) (/.f32 #s(literal 1 binary32) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
	98.0%	(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
	94.7%	(.f32 (+.f32 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))))
	94.8%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
	65.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
	65.6%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (PI.f32)) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (log.f32 alpha))))
	94.9%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
	94.7%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (fma.f32 (/.f32 #s(literal 1/2 binary32) (log.f32 alpha)) (/.f32 (.f32 alpha alpha) (PI.f32)) (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))))))
	97.1%	#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))

Compiler

Compiled 5 124 to 1 508 computations (70.6% saved)

regimes123.0ms (1.8%)

Memory

-17.6MiB live, 182.9MiB allocated; 28ms collecting garbage

Counts

83 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
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#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 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 1 (* cosTheta cosTheta)))) (.f32 (fma.f32 (/.f32 (fma.f32 (/.f32 cosTheta (pow.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) #s(literal 2 binary32))) (/.f32 cosTheta (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (PI.f32)))) (neg.f32 (log.f32 alpha))) #s(literal -1/2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 alpha alpha) (PI.f32))) (.f32 (neg.f32 (log.f32 alpha)) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))) (*.f32 alpha alpha))))
(/.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))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (fma.f32 (pow.f32 cosTheta #s(literal 6 binary32)) (pow.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(literal 3 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 cosTheta cosTheta) (-.f32 (pow.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 2 binary32)) (fma.f32 alpha alpha #s(literal -1 binary32))) #s(literal 1 binary32)))))
(/.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) (cbrt.f32 (PI.f32))) (pow.f32 (cbrt.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))))

Outputs

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

Calls

4 calls:

51.0ms	cosTheta
23.0ms	(/.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))))
23.0ms	(*.f32 alpha alpha)
22.0ms	alpha

Results

Accuracy	Segments	Branch
98.7%	1	`(*.f32 alpha alpha)`
98.7%	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))))`
98.7%	1	`cosTheta`
98.7%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes104.0ms (1.5%)

Memory

-13.2MiB live, 86.0MiB allocated; 9ms collecting garbage

Counts

57 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (log (pow (* alpha 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 #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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.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)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #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)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 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))))
(/.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 (fma.f32 (-.f32 alpha #s(literal 1 binary32)) alpha (.f32 (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (-.f32 (*.f32 alpha alpha) #s(literal 1 binary32)) cosTheta) cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (.f32 #s(approx ( (- 1 (/ (/ 1 alpha) alpha)) alpha) (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) alpha)) alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.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 (.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 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.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 #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 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (.f32 (-.f32 (fma.f32 alpha alpha (/.f32 #s(literal 1 binary32) (*.f32 cosTheta cosTheta))) #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))) #s(approx (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)) (.f32 (fma.f32 cosTheta cosTheta (/.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 alpha alpha))) (.f32 alpha alpha)))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(/.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 #s(literal 1 binary32) alpha) (/.f32 (-.f32 alpha #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (*.f32 (/.f32 (PI.f32) #s(literal 2 binary32)) (log.f32 (pow.f32 alpha #s(literal 4 binary32))))))
(/.f32 (/.f32 (-.f32 (pow.f32 alpha #s(literal 4 binary32)) #s(literal 1 binary32)) (fma.f32 alpha alpha #s(literal 1 binary32))) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #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))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) (/.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))))

Outputs

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

Calls

4 calls:

15.0ms	cosTheta
14.0ms	alpha
14.0ms	(/.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))))
14.0ms	(*.f32 alpha alpha)

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)

regimes42.0ms (0.6%)

Memory

18.6MiB live, 62.4MiB allocated; 5ms collecting garbage

Counts

37 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (log (pow (* alpha 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 #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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.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)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (*.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #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)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 (*.f32 alpha alpha)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))

Outputs

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

Calls

4 calls:

13.0ms	cosTheta
9.0ms	(*.f32 alpha alpha)
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))))
9.0ms	alpha

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes36.0ms (0.5%)

Memory

19.5MiB live, 62.6MiB allocated; 5ms collecting garbage

Counts

32 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (log (pow (* alpha 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 #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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (.f32 (fma.f32 (.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) cosTheta) cosTheta #s(literal 1 binary32)) (PI.f32)) (log.f32 (.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)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes36.0ms (0.5%)

Memory

-3.7MiB live, 41.1MiB allocated; 5ms collecting garbage

Counts

30 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (.f32 cosTheta (fma.f32 alpha alpha #s(literal -1 binary32))) cosTheta #s(literal 1 binary32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (log (pow (* alpha 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 #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 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx (* cosTheta (+ (* alpha cosTheta) cosTheta)) (*.f32 cosTheta cosTheta)) (-.f32 alpha #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 (+.f32 #s(literal 1 binary32) alpha) (fma.f32 alpha alpha #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

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:

11.0ms	cosTheta
8.0ms	alpha
8.0ms	(/.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)

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)

regimes62.0ms (0.9%)

Memory

-8.8MiB live, 45.7MiB allocated; 15ms collecting garbage

Counts

23 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha 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)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) (.f32 (.f32 (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta)) (.f32 #s(literal 2 binary32) (PI.f32))) (log.f32 alpha))))

Outputs

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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:

42.0ms	(/.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
6.0ms	cosTheta

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes62.0ms (0.9%)

Memory

2.0MiB live, 47.1MiB allocated; 4ms collecting garbage

Counts

20 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (log (pow (* alpha alpha) (PI))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta))) #s(approx (* (* 2 (PI)) (* (- 1 (* cosTheta cosTheta)) (log alpha))) (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 #s(literal -2 binary32) (*.f32 cosTheta cosTheta) #s(literal 2 binary32))))))

Outputs

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

Calls

4 calls:

44.0ms	(*.f32 alpha alpha)
6.0ms	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))))
5.0ms	alpha

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes46.0ms (0.7%)

Memory

2.0MiB live, 47.0MiB allocated; 5ms collecting garbage

Counts

19 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))
(/.f32 #s(approx (- (* alpha alpha) 1) (fma.f32 alpha alpha #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.f32 cosTheta)) cosTheta #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

29.0ms	(/.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))))
5.0ms	(*.f32 alpha alpha)
5.0ms	alpha
5.0ms	cosTheta

Results

Accuracy	Segments	Branch
97.2%	1	`(*.f32 alpha alpha)`
97.2%	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))))`
97.2%	1	`cosTheta`
97.2%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes24.0ms (0.4%)

Memory

13.2MiB live, 55.1MiB allocated; 7ms collecting garbage

Counts

18 → 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (.f32 (log.f32 alpha) #s(literal 2 binary32)) (PI.f32))))
(/.f32 (.f32 (-.f32 alpha #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) alpha)) #s(approx ( (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
#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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (log (pow (* alpha 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 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 #s(approx ( cosTheta (+ (* alpha alpha) -1)) (neg.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)) #s(literal 1 binary32))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ 1 (* (* (- (* alpha alpha) 1) cosTheta) cosTheta)))) #s(approx (+ (* (* 1/2 (/ (+ (/ (/ 1 (PI)) (- 1 (* cosTheta cosTheta))) (/ (/ (* cosTheta cosTheta) (PI)) (pow (- 1 (* cosTheta cosTheta)) 2))) (log alpha))) (* alpha alpha)) (/ (/ -1/2 (* (log alpha) (PI))) (- 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) (* (* (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))) (+ (* (* cosTheta (+ (* alpha alpha) -1)) cosTheta) 1))) (/.f32 (/.f32 (-.f32 (.f32 alpha alpha) #s(literal 1 binary32)) (PI.f32)) (log.f32 (.f32 alpha alpha))))
#s(approx (/ (- (* alpha alpha) 1) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.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) (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1))) (/.f32 (/.f32 #s(literal -1/2 binary32) (.f32 (log.f32 alpha) (PI.f32))) (-.f32 #s(literal 1 binary32) (.f32 cosTheta cosTheta))))

Outputs

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

Calls

4 calls:

8.0ms	alpha
5.0ms	cosTheta
5.0ms	(/.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))))
5.0ms	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

regimes8.0ms (0.1%)

Memory

18.8MiB live, 18.8MiB allocated; 0ms 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))))
(/.f32 #s(approx (- (* alpha alpha) 1) #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))
(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))

Outputs

(/.f32 (fma.f32 alpha alpha #s(literal -1 binary32)) #s(approx (* (* (PI) (log (* alpha alpha))) (+ (* (* cosTheta (+ (* alpha cosTheta) cosTheta)) (- alpha 1)) 1)) (*.f32 (log.f32 (*.f32 alpha 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	alpha
2.0ms	(*.f32 alpha alpha)
2.0ms	cosTheta

Results

Accuracy	Segments	Branch
94.9%	1	`(*.f32 alpha alpha)`
94.9%	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))))`
94.9%	1	`cosTheta`
94.9%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes13.0ms (0.2%)

Memory

-44.6MiB live, 11.5MiB allocated; 9ms collecting garbage

Counts

3 → 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))))

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

Outputs

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

Calls

4 calls:

8.0ms	alpha
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))))
1.0ms	cosTheta
1.0ms	(*.f32 alpha alpha)

Results

Accuracy	Segments	Branch
64.2%	1	`(*.f32 alpha alpha)`
64.2%	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))))`
64.2%	1	`cosTheta`
64.2%	1	`alpha`

Compiler

Compiled 29 to 20 computations (31% saved)

regimes5.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB 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 (-.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	cosTheta
1.0ms	alpha
1.0ms	(*.f32 alpha alpha)

Results

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

Compiler

Compiled 29 to 20 computations (31% saved)

simplify17.0ms (0.2%)

Memory

-7.5MiB live, 34.6MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Stop Event

1×	iter limit
1×	unsound

Calls

Call 1

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

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

derivations1.1s (16.3%)

Memory

2.4MiB live, 1 056.6MiB allocated; 184ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1450
1	572	1398
2	2417	1236
0	8614	1182
0	613	4823
1	2033	4375
0	8648	4205
0	13	65
0	23	65
1	101	65
2	818	63
0	8860	55
0	67	462
0	107	447
1	438	424
2	3497	424
0	8315	413
0	535	4139
1	1642	3890
2	7115	3890
0	8667	3778
0	608	4827
1	2009	4366
0	9340	4207

Stop Event

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

Compiler

Compiled 399 to 103 computations (74.2% saved)

preprocess72.0ms (1%)

Memory

-5.1MiB live, 92.3MiB allocated; 6ms collecting garbage

Remove

(abs cosTheta)

(abs alpha)

Compiler

Compiled 1 018 to 340 computations (66.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze84.0ms (1.2%)

sample1.7s (24.7%)

explain193.0ms (2.8%)

preprocess135.0ms (2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify104.0ms (1.5%)

localize57.0ms (0.8%)

series110.0ms (1.6%)

simplify145.0ms (2.1%)

rewrite171.0ms (2.5%)

eval73.0ms (1.1%)

prune47.0ms (0.7%)

simplify9.0ms (0.1%)

localize200.0ms (2.9%)

series168.0ms (2.4%)

simplify170.0ms (2.5%)

rewrite48.0ms (0.7%)

eval35.0ms (0.5%)

prune31.0ms (0.4%)

simplify8.0ms (0.1%)

localize154.0ms (2.2%)

series76.0ms (1.1%)

simplify162.0ms (2.4%)

rewrite17.0ms (0.2%)

eval21.0ms (0.3%)

prune36.0ms (0.5%)

simplify201.0ms (2.9%)

localize203.0ms (3%)

series155.0ms (2.3%)

simplify241.0ms (3.5%)

rewrite155.0ms (2.3%)

eval136.0ms (2%)

prune64.0ms (0.9%)

regimes123.0ms (1.8%)

regimes104.0ms (1.5%)

regimes42.0ms (0.6%)

regimes36.0ms (0.5%)

regimes36.0ms (0.5%)

regimes62.0ms (0.9%)

regimes62.0ms (0.9%)

regimes46.0ms (0.7%)

regimes24.0ms (0.4%)

regimes8.0ms (0.1%)

regimes13.0ms (0.2%)

regimes5.0ms (0.1%)

simplify17.0ms (0.2%)

derivations1.1s (16.3%)

preprocess72.0ms (1%)

end0.0ms (0%)

Profiling